I found this very brief document about traveling with bicycles on the French train system.  I'm posting a link here in case it's useful to anyone.

https://eurovelo3.fr/int1/assets/pdf/Guide-trainve-lo.juillet-2023-11.pdf

The document is in French but you can run it through Google Translate (translate.google.com) and get a reasonably good translation into the language of your choice.  Including Esperanto, apparently!

I wouldn't expect this information to be valid for a long time.  If you're planning to travel in France with your bicycle in 2024, it might be a good idea to check back on that site next spring.  Things are changing (usually for the better) with respect to bikes on trains in France, despite the SNCFs basically bike-hostile attitude.

Thank you for posting this, was happy to see TGV from Lyon to Paris takes assembled bikes.

I thought this was going to be a SNCF document, and was immediately pleased by its candid and friendly tone. 

p.s. Is there a reason to use Trainline rather than DB or SNCF?

I would defer to anyone who's actually used Trainline.  But given how difficult it is to travel on the SNCF with their own tickets, I wouldn't attempt to use anything other than the SNCF site for booking.  I have no experience with DB.

It's a great place to mention one of the most amazing trains for cyclists we have seen so far. I've seen that some of you cycled the Loire by Bike cycle route, so maybe you had an occasion to see it.

It is called the Train Vélo Loire and it operates along the railway line following the Loire - from Orleans through Blois, Saumur, Angers and Nantes, to Le Croisic near Saint-Nazaire. It is free of charge for bicycles, as the most of TER trains in France. And you don't need a reservation. And it runs from June to September.

These trains carry from 33 to 83 (!) bicycles, depends of the time of the year.

And it was quite amazing moment, when the woman in the railway uniform came out of a train and led herself our bicycles to the bicycle compartment on the lower level of a regional double-decker. 

It was one of the last scenes during our cycling tour along the Loire Valley.

S.