Clermont-Ferrand and the surrounding area, especially between CF and Ambert and also down towards Mont Dore are superb.
The area towards Mont Dore is very steep extinct volcanoes, and a lot of it a National Park so it’s great for road work but may not be doable due to restrictions or it’s severity.
We have based ourselves in a small town called Cunhalt (pronounced Kai-ack) in the past at a very nice thee gite house. The owners are bikers and their Mum and Dad run the property in Cunhalt for them (they also own a Pub, which they run themselves in The Peak District).
There are a lot of forest , piste style, roads in the area that would be doable on a GS, there also a lot of more difficult stuff if you’ve the experience.
It’s not a long ride to get to either the Ardeche or over to the Cruse/Limousan areas from there. Both areas are also great for bikes.
There was a company, run by an English couple, just North-West of CF that did guided off road stuff with accommodation but I can’t find a link at the moment.
This is what the area around Cunhalt is like, you can ride almost every trail in the area you can see in the photos:
There is a quad hire place in Cunhalt and the guy there is very happy to advise on where you can and can’t ride, he even has maps. You’ll need a fluent French speaker as he speaks no English at all.
It would be worth your while getting in touch with Bill at Mission Motos, he’s based a lot further south but has a great site with loads of links and also may have much more up to date info then me.
Here’s a link to his site:
http://www.missionmotos.biz/
Heres a link to a bike hire place in the area. They may help you as well:
http://www.tenerespirit.com/multimedia.php?id_media=102&titol=WR adventures in Auvergne