Tranporting your bike with a bicycle bag (‘housse’).
Perhaps the best way to transport a bicycle is with a bicycle bag (une housse). They can be purchased at most bicycle stores (GoSport; Decathlon) in any of the malls that ring Paris (YES, the French have malls; eg Chelles; take the train from the Gare de l’Est), or from the BHV store opposite the Mairie/Town Hall right in the centre of Paris. You will also need to purchase, if you don’t have one already, a key or wrench/spanner that will allow you to detach the handle bars/guidon of your bike. If arriving from North America without a housse, you should allow one day in Paris for the purpose of buying one.
At first sight it may not seem feasible to get your bike into the bag, but it is indeed possible (turn the front forks so they face to the rear of the bike). You do not need to remove the pedals. Your bike should however have quick release brakes and wheels.
Notes:
Add the SNCF web site and instructions on how to use.