If normal trains will take bikes, could you not get the train to Folkestone, ride to the Eurotunnel terminal, head over there then back on the french trains in Calais? Bit faffy but no disassembly required
Quite a few TGVs require dissembled bikes so this method ends up quite a lot slower.
I’m on an Interrail trip in Europe right now, and last week we took the TGV from Paris Gare de Lyon to Barcelona. It was very busy, lots of people with lots of luggage, and while we were boarding I was thinking it would be a massive pain with a bike in a bag. On our onward train to Madrid someone did actually have a bagged up bike, and he was keeping it in the cafe car.
I’ve found that when travelling with my bike by train I need to be <ahem> assertive about getting my bike on board, either in a bag or assembled. Usually moving a load of pink wheely suitcases out of the bike space.