I don’t know about the trails to Lindaret, but the path from the top of the bike park lifts to Col de Bassachaux is marked very explicitly as walkers only – weather that bothers you is up to you. It’ also very technical – bit like UK technical – rocks and drops rather than fast with berms though and I expect some would need walked up at least.
The GR5 from there is quite technical at first before becoming double track into the Nature reserve park (where the big mountain is, can’t remember what it’s called, but it’s fairly obvious being huge and all). To get back to Chatel is either down into the same valley Pre la Joux is in (steep, non technical), straight to Chatel there are two ways – one is ultra difficult, and the other is a series of steep switchbacks through the woods that drops straight down the mountain. The GR5 is also very steep and takes you just beneath Chatel – I’ve only seen it from the top and it looked a bit mad.
If you get the French equivalent of an OS map of the area all of these trails are very very well marked.
There’s loads of walking trails that would make superb natural riding though – much of it very technical. The problem (for me at least) was that quite often it becomes too difficult very quickly!
I am crap though – if you’re good, there’s some great potential – and you’d be away from the Brits-abroad-storm-trooper set…