Do European train bookings include reserved seats on a specific train departure?

Specifically for the IC from Brussels to Luxembourg City. This is the IC 21xx (with xx a sequence number for the nth train of the day starting at 04 for that train line). You can look up the exact schedule on the Belgian railway website (select the train radiobutton and enter your train line, f.e. IC2110). Date is optional, but recommended as some trains have different schedules in weekends and on holidays.

This is a standard Belgian IC train and does not have seat reservation or specific time requirements. Your ticket is very likely counted as a standard ticket (not 100% because booked through SNCF and not SNCB). The general conditions for this type of ticket are: valid on the date (you can get on any train that day) printed on the ticket and you are allowed to get off at any stop on that line and get on a later train on the same line (this is a recent change in conditions). So you can visit any cities in between, should you want to. You can find the conditions at the bottom of the page I linked to for standard ticket, but they are only available in french and dutch.

Optional information:
For future reference, when travelling through Belgium, it can be more interesting financially to use several tickets with linked destinations to reduce your travel costs. In this case, I would have suggested to take a ticket from Brussels to Arlon (Arlon being the last stop in Belgium) and a ticket from Arlon to Luxembourg. This comes out slightly cheaper in general (few euros usually). However, if you are under 26 or travel frequently in Belgium, you can take advantages of significantly cheaper rides using GoPass 1 or GoPass 10 (under 26) or RailPass (over 26, at least 10 trips). Return trips are also cheaper in the weekend (if the return happens in the same weekend).

As already pointed out in multiple comments this is very country specific and based on your description I cannot tell to which country do you travel. I can only rule out few.

Yet since you have received your (printed) tickets it means you are eligible to take a trip as long as you go according to the validity dates and destinations on the ticket. Since your tickets do not have specific time schedule, just validity dates and destinations most probably you are eligible to take any train in that range and most probably there is no seat reservation available for the trains you have selected. It might be that there is a seat reservation but it is optional and paid additionally.

While very unlikely, sometimes the rules for tickets sold abroad are different than tickets sold locally and your situation might be that you do not get a specific seat reservation despite regular country tickets have them. In such case you get trip flexibility at the cost that there might be no seat available for you. Usually it will mean you’ll have to stand part of entire trip if no free seats are available. There are some trains (like EIP in Poland and possibly some other high speed trains across Europe) where you will not be allowed without seat reservation, but I expect for those trains you would get ticket with seat assignment included.

So in general, as long as you have tickets and their validity meets your needs, you’re good to go with trains of your choice, possibly with some additional flexibility.

You mentioned your schedule is quite tight so your other concern might be delays. Here the situation is a bit trickier. There is an EU law that gives a passenger a number of rights (all listed here). Some of them include:

• be transported to your final destination at the earliest opportunity (or a later date of your choosing). This includes alternative transport when the train is blocked and the service is suspended.
• meals and refreshments (proportionate to the waiting time)
• accommodation – if you have to stay overnight.

Specific local implementation vary in EU member countries, for example in Poland law enforces train operators to ensure that in case of a delay you can continue your travel on the same day. So if your next connection is the last day to the destination on that day this next connection has to wait regardless how long the delay is. If the next connection isn’t the last train to the destination on that day it’s on railroad company discretion to decide what to do (in some countries it might vary and rules might be more strict for the railroad enforcing it to delay next connection anyway). It might be different in other countries and, as pointed out by Willeke sometimes you just get money for a taxi to your destination.

Anyway in such case it is good to check with the train crew if the next train can also be delayed allowing you to change.

I don’t know about other countries but for instance in Poland you are entitled to rebook your ticket for a different schedule (within some timeframe, but it’s something like 30 days if I recall correctly) at no cost.

Also since you bought all your tickets from a single travel agent (webpage) and as I understand in one transaction these rights for package travel also apply to you (unless all tickets are on the same day):

The organiser is responsible for the proper performance of all travel services included in your package.

If a travel service can’t be provided as agreed, for example if a provider can’t carry out an agreed service or can’t do so in the agreed form (such as providing transport to or from your destination, providing the agreed type of accommodation, or carrying out a guided tour that you booked), the organiser has to resolve the problem at no extra cost to you.

If it is impossible to make alternative arrangements or you reject the arrangements offered to you on valid grounds, and the package includes your transport (such as air travel), the organiser must offer to repatriate you. If the travel services do not reach the agreed standards and this cannot be resolved on the spot, you may also be entitled to compensation.

You are also protected if for whatever reasons you cannot perform your trip due to the incorrectly issued tickets (on the same page):

When you book a holiday, the responsible trader (the travel agent or online travel agency) is liable if any of the following occurs during the booking process:

• errors made by the retailer if they are responsible for arranging the booking of a package or of travel services which are part of linked travel arrangements

The page does not state details about the liability.

Note that those last two excerpts state the liability of the ticket retailer, so the webpage where you booked your tickets. As you can see you’re double-protected, at least that someone will either have to take you to your final destination (either train company or ticket retailer). Note that the liability (especially in case of tight schedule) is limited to reaching destination only (so it might be you’ll be rerouted and miss some of the intermediary targets) and there might be rules limiting the liability if you left yourself inadequate time for a change.

Please note – all those rules apply in EU. Not all European countries are members of EU! Yet majority is and you can easily check that. Also country might decide not to apply those rules for local connections but since you’re referring to IC tickets that’s probably also not the case.

Edit based on the specific trip leg provided by OP and some extra research

I couldn’t find details about operator that operates the Brussels – Luxembourg trip but I’ve checked conditions on various sites (SNCF, SNCB, RailEurope). Each of those pages gives you specific details about fare for each train. For this specific train the fare is open, meaning you can choose any train within the given range of dates. Also on this route there is no seat reservation offered, which means in general you’re free to choose any seat available (within your class of course) and once seated you cannot be requested to leave your seat by someone claiming to have seat reservation (unless you pick a special seat that in general is reserved for pregnant women, mother with children or people with some disabilities – check the stickers over the seats that informs about that and I suggest – avoid those seats). Moreover Rail Europe claims the ticket is valid for 15 days, giving you a huuuge flexibility:

From BRUXELLES NORD BR To LUXEMBOURG LUX

Eurocities 2106 – Reservation not included

1 x Ind. Open Ticket Adult

European open ticket must be used within the 15 days validity period. Journey might be effected on any date within the period of validity. Open Tickets do not guarantee a seat, thus reservations are highly recommended. Important: Reservations are mandatory on most of high speed, scenic trains and all night trains.

The scripted highlight is mine.

Also the same train checked on SNCB page (that is IMO most accurate for this particular leg – I believe this is the actual operator of this specific train, but it’s just a best guess based on my knowledge of regional transport) shows those conditions (to obtain it simply use the trip planner and follow with the ticket purchase up until you have a specific train selected):

Bruxelles-Midi/Brussel-Zuid – Luxembourg € 43.60

Adult (26-59): 1 € 43.60 per person

Flex Fare Adult 2nd Class

Special information: Ticket valid for any conventional train on the requested route during the whole validity period of the ticket (for homeprinted tickets, the validity period is limited to the requested travel date). Not valid on high-speed trains, except for ICE trains.

Refund Conditions: Refund possible for tickets presented up to the first day of validity. After the first day of validity, non refundable.

Exchange Conditions: No exchange possible

Travel Conditions: no specific travel conditions. ATTENTION: homeprint tickets have a validity of 1 day!

Again, scripted highlight is mine.

On this SNCB page about passenger rights you can read more about carrier specific implementation of those rights described earlier. I’ll not quote it here, as this will lead you to the most up-to-date terms and in case of any changes in the future the quote might become misleading.

Finally this nice SNCB page about terms and conditions provides links to many carriers T&C details that should provide final, definite information if you’re still in doubt. I just need to warn you, that it’s sometimes not so obvious to find out which specific fare conditions apply and some of the pages are available in the carrier language only.

One last remark – it is often possible to buy a ticked without seat reservation for a train with either optional or mandatory seat reservation. In most cases (from my experience all trains other than high-speed and some express class, definitely all the standard ones that will be marked just with IC in the train number) such ticket is enough to have a trip and usually it gives you a possibility to obtain a seat reservation (for free if it is compulsory for a one-trip tickets bought directly at the carrier, paid if the reservation is optional or mandatory but paid additionally – not sure if this option is still used anywhere but yes, there was something like that in the past). The channel to obtain such seat reservation depends on your ticket and a carrier, in general you should be good to get it any any counter selling the tickets of that carrier, and for sure in the country of the operator.

If the seat reservation is not possible with a regular fare for that route you’ll not be able to get it in any way for other than standard tickets as well.

If for some specific leg you’re still unsure or can’t find the details as I show here, try calling the carrier in the country of train departure. They will for sure be able to give you most accurate details given you provide the train number you plan to go with.

I know Dutch and British trains (with some exceptions, like ICE, TGV, and some other international trains) have no reserved seats anywhere.
I think it’s the same in Belgium, Germany, and probably elsewhere from what I’ve seen of their train services (which isn’t all that much, thank god, I hate trains in general).

Certainly on Dutch trains (again, ICE and TGV excepted, as well as international trains BUT only for the international segment of the trip) you don’t buy a ticket for a specific train either, but for a specific day (or even a ticket without a date). Again, in my experience elsewhere it’s pretty much the same there. E.g. I’ve traveled by train in the UK and just as in the Netherlands the ticket just states the city pairs and the date(s) on which the ticket is valid.

In this way European trains are much more like a bus service than an airline service, and the service level available to passengers reflects this with usually no catering, very limited if any toilets, and regular overcrowding.

From what you said, you can expect that you do not have a reservation.

On TGV/Thalys you are (usually) required to have a seat reservation, so whenever you buy a ticket, you kinda automatically have one (otherwise you can’t get a ticket). The seat number is printed on the ticket.

On ICE (note the “E”) which is the better, faster “express” version of IC with approx. 1/3 as many stops and running at approx. 2x cruise speed, you (usually) get reservation for free and automatically in first class, but in second class you do not get it automatically. You have to book it explicitly, and it will cost you some 4-5€ extra, but I would absolutely recommend it because some ICEs are full to the last seat, and nothing sucks more than having to stand, or stay in the restaurant wagon (if there’s one) for 4 hours.
I wouldn’t know for sure about seat reservations for first class in IC (without “E”), the tree or four times I’ve travelled IC in my life, it was 2nd class, and seat reservation was (of course) extra.

In any case, the wagon and seat number is printed on the ticket if you have a reservation (if there’s none, you don’t have one).

Further steps to take would be to reserve a seat, which can be done online. Note that depending on what country you do it in, and depending on what alternative carriers are involved, it can be adventurous (for example, two years ago I learned that booking with Bahn and going to Italy would much to my surprise work just fine with the Italians, but the Austrians would give me trouble for the short segment in between. Same physical train, different carrier. Hey, if anything, you’d think it wouldn’t work on the Italian end, but that was actually no issue at all.).

It is generally possible to buy tickets without seat, and funnily enough to reserve seats without a ticket. This seems nonsensical, but since there are tickets that are valid on several days (virtually unlimited, even) and subscriptions that allow 100% free of charge travel in at least some countries, this actually makes sense. Those people having e.g. one of the 100% reduced fare subscriptions would just book a seat when they wish to travel.

About “tight schedule”, I’d like to warn you. This is not the best possible approach in combination with “train”, in particular IC. There’s countries which are arguably somewhat better, and some which are definitively not among the better ones, and it’s not always obvious. IC per se is on the more unreliable side due to having many stops and being a lower-priority train. If you have a tight schedule, ICE/TGV may be a better choice (although I’ve had a 2 hours delay on a 3 hour trip on German ICE already, too).
You mentioned Belgium-Luxemburg being the first segment. My personal experience with Belgium is that you stand at the station and no train is to be seen. As you get more and more nervous and ask staff about it, they’ll say “Yeah sure, that train leaves in 2 minutes. But not today.”. When you ask when the next train will leave, they’ll tell you: “Tomorrow morning at 6:14”. Yup, Brussels, capital of Europe.

So… tight schedule may work, but it may not be the best plan.

It really depends on the country/train, IC is a code used in different countries for long-distance non-high-speed trains with slightly different rules. Generally speaking, those trains have either no seat reservations or optional seat reservations (but no mandatory seat reservations).

Therefore I would assume you do have a ticket that’s valid on your chosen trains. In some cases, seat reservations are available but not mandatory and open tickets do not mention the train for that reason. For the one specific route you mentioned, seat reservations are simply not available on IC trains at all. If you’re really concerned about finding a seat, you could book a first class ticket. It doesn’t guarantee anything either but there is usually more space in first class.

Where available, it is certainly possible to book a seat reservation separately but that’s usually not possible online (the German railways do sell them online).