I have used a fancy Fairmean bag on TGV while someone I was riding with used binbags, both worked.
I was more interested in where rather than how. I'll have a bike bag with me anyway as I'm coming from a riding trip to work.
The Vercors and/or Chartreuse massifs would be my recommendation. Both easily accessible by train and both have quiet and challenging roads but are low enough in altitude terms to likely be fully open at that time of year.
ah! for MTB I have no idea, I have planned a few roadie trips with TGV though, they are quite painless.
@atz started
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I have used a fancy Fairmean bag on TGV while someone I was riding with used binbags, both worked.