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Give it to @scherrit :)
In the past when I've used TGV I've bagged the bike (proper bag, but you can get cheap, lightweight ones that'll do) but I was going to use a clingfilm wrap like I saw a Dutch guy do - wheels off, seatpost out, wrap everything in cling film and throw it on one of their shelves.
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There are limited numbers of bike spaces which you can book beforehand and can then take your bike asis - I did this last year, worth getting on this as soon as bookings open. Did this coming back from Brest last year and also had couple of other TCR riders that just blagged it with the conductor, and we just stacked them on top as they were bagged/boxed up, but YMMV.
https://www.seat61.com/France.htm has some good info on train routes.
Last year I got a TGV back to Paris then Eurostar to Euston St Pancras Kings Cross Whatever The Fck