Clermont Ferrand is in the middle of the Massif Central, there should be loads of trails – there are a few small ski resorts nearby – no personal experience as only road ridden there
Yes, there are, I spent a week as part of a group riding all around that area, stopping in gîtes every night. There’s loads of trails around there, most of the roads we rode were incredibly well surfaced and with very little traffic as well. I can’t remember specifics now, it was back in 1997, literally during the whole Princess Diana thing, so we were pretty much isolated from all the hysteria surrounding it.
I remember we started off in Clairmont-Ferrand , and Orcines and Puy de Dôme were part of the route. Some of the trails required some significant scrambling up steep climbs hauling ourselves up by holding onto trees, while dragging our bikes up with us, but the majority was riding off-road through a lot of stunning scenery. I think I took my Cannondale M800 Beast-of-the-East, which had a pair of original orange Bombers fitted, which it absolutely owned! Had a set of early Hope discs on as well.
Somewhere I’ve got some photos, but they’re prints, taken with a very basic point’n’shoot plastic camera, and I’ve no idea where they are now. I don’t think you’ll struggle to find a lot of good riding on the GR routes.