-
TGVs all have different bike rules. You can take whole bikes on some but you can go up to 120cm on any in a bag/box - which would mean both wheels out but nothing worse.
See here. https://www.freewheelingfrance.com/planning-a-trip/bikes-and-french-trains.html
"Bagged or boxed bikes on TGVs: Bikes can travel free of charge on all TGVs if they are bagged or boxed. You simply place your bagged/boxed bike in the luggage area as you would a suitcase. The size limit for bagged/boxed bikes is 120cm x 90cm but I've never heard of anyone's bag being measured or anyone being stopped for an oversized bag."
You can, going against the rush hour - I've done it both ways recently.