Upvote:0
If you connect from an 'international' flight (outside Schengen area) to another 'international' flight in the same airport, you can stay within the International Transit Area. Your luggage will be checked through, if your flights are booked on one ticket.
You do not have to leave the international transit zone - it would be a voluntary decision by you to walk out of it (and there is immigration control at the exit, so you can't accidentally walk out). The Transit area is legally considered to not be a part of France, so you never 'enter' France if you stay in it.
Upvote:2
Even though you plan to buy both legs in a single transaction, Kiwi.com is known to sell separate tickets as if they were a single ticket, and as I doubt Tuifly and French Bee interline, it is nearly certain that they are really two different bookings, and you won't be able to do through check-in (getting both boarding passes at once, and having hold luggage transferred to the next flight for you).
However, given that:
There should be no need for you to got landside, and you should be able to remain airside (in the "international zone" / "transit area"). You shouldn't have to go through immigration (passport control), and shouldn't need a valid visa for France.
As you are US citizens, you don't need an airport transit visa either.
I would however double-check:
that you can indeed check-in online for your flight to the US. Some airlines have specific policies for US-bound flights and won't issue online boarding passes for those flights. Call the airline to check. Alternatively, they may have transfer desks in the transit area which would allow you to get a boarding pass once you get to Orly. Again, check with them if that's needed and available.
that there is indeed sterile transit at Orly Sud in your situation. It should be the case according to the airport operator's site, but there's always a possible exception (I believe Orly sees a lot less international-to-international transit than CDG does, so you never know if some works or changes could make it more difficult). You can reach ADP here or by phone: +33 1 70 36 39 50.
Note that when you board the first flight, the airline will consider that your final destination will be Paris. I don't think they would go as far as counting the days you spent in the Schengen Area, but just in case, make sure you have documentation available to show you have an outbound flight the same day from the same airport and terminal.