Yes. However, to travel for your bike for free on a TGV you need to first dismantle it and place it in a bike bag. You also need to check the dimensions. The bike bag needs to fit in the luggage compartment on the TGV. You are able to take your bike on a TGV without dismantling it. However, to do this you will need to pre-book and pay €10 per bike. We put together an article with more details about taking a bike on a TGV based on our own experiences.