Is a picnic at the Chateau de Versailles possible?

Just to complete the answers:

Can I exit the palace and then re-enter after purchasing my food?

No, at least it was not possible when I last went there (September 2014).

The reason is most likely because it is not possible to verify that the same person who is leaving is the person coming back. Tickets are not registered to a given name (otherwise, checking all of them would take inordinate amounts of time). Therefore, you would be able to visit the château in the morning, leave it, and then re-sell/give your used ticket to another person. To avoid that, they disallow re-entering using the same ticket.

Conclusion: unless you are exempt (i.e. EU residents < 25 years old) and willing to re-queue, you cannot leave to buy food.

BTW, the food indoors is quite expensive: sandwiches were about 8€ IIRC. There’s also a restaurant indoors, but I dared not check the prices.

You have several possibilities for a picnic on a normal day (as Gayot Fow’s answer mentions, the white picnic is worth the trip as well).

The first one is where everyone goes, particularly tourists – namely around the Grand Canal. I would not say that you need to "reserve" your spot but some places get crowded.

A picture I took in May, on a Sunday, from the left bank of the canal, where the Allée des Matelots meets the Grand Canal (showing the "crowded areas" above):

There is another place, where locals tend to picnic (more than tourists); This is also a typical place for children birthdays, starting from May

I would not recommend any of the boulangeries – they are great for bread but will be horribly overpriced for a picnic. Better bring in stuff yourself, there are supermarkets nearby (the closest will probably be Leader Price or Super U which is not that far either). There are others too but I know that side of the gardens better 🙂

You can now drive into the Versailles Gardens ($$), which can be practical if you need to carry a picnic for 27 people.

UPDATE as promised

You have a few places where you need to pay in the Versailles castle:

• the castle itself (with long waiting lines)
• the gardens right in front of the castle (on the other side). You can access them either from the side of the castle, or from the other side (there are two ticket booths on the path from the Grand Canal to the gardens). BTW access if free during winter times.
• the Hameau de la Reine, a little village built for Marie-Antoinette, worth the walk.
• the Trianons (small castles)

You probably can bundle some of these, I do not know because when I was actually visiting Versailles all of this was free and now I walk or ride on the free part 🙂

A rough map of the pay vs free areas (I missed the Trianon in the pay area). The line in blue are the roads where you can drive.

If you had to make a hard choice I would go for the Hameau de la Reine which is unusual. Still, the castle is nice, the gardens are nice too. It really depends on the time you have.

You can also rent bikes at the entrances of the garden.

There are light and sound concerts in the evenings during spring, summmer and automn – I do not know if they are nice, at least the sound and the fireworks are OK (seen from the outside) I finally attended to one of the fireworks. It is definitely worth it – you walk in places that are usually closed for two hours or so, there are some water shows and when night falls down – fireworks. I would say that the fireworks part is the lest interesting one (standard fireworks) but the overall atmosphere is great.

All in all Versailles is a fantastic city.

Of course you can picnic at Versailles, it’s de rigueur; in the gardens behind the palace that is (not inside). You can picnic all year around whenever the gardens are open to the public. In the summer the only problem is finding a suitable spot because the competition from other people having a picnic can be quite keen. Pick your spot early and lay a blanket down to ‘reserve’ it as soon as you arrive in the morning. Europeans will generally respect the ‘reservation’, especially the British and German tourists.

On Bastille Day, the 14th of July, a wonderful “Déjeuner sur l’Herbe”
is organized in the gardens of the Palace of Versailles. Thousands of
people come together with their picnic baskets and have a festive meal
on the banks of the Grand Canal. In English it is known as the Picnic
of Versailles or the White Picnic (“pique-nique en blanc”), since
white is the dress code.

Source: http://paulsmit.smugmug.com/Features/Europe/France-White-Picnic-Versailles/22215509_7fWhWg/1775525267_SWmth3T#!i=1775525267&k=SWmth3T

You need about one day to see Versailles gardens, but you will only
see the essentials. And we tell you that from experience. The gardens
of Versailles are incredible big and beautiful, a blend between nature
and culture. You can have long walks, rent a boat, admire the
sculptures and flowers, have picnics with friends, listen to the
musical fountains and

Source: http://allonfrance.com/versailles-gardens-a-blend-between-culture-and-nature/

For your last question: the best option is to eat a very large breakfast before you enter the grounds. Don’t drink too much wine at mid-day because it will slow you down and dull your senses. The boulangeries in the surrounding neighbourhood are very upmarket; try to get your stuff in one of the arrondissments beforehand.