Between Avignon and the Luberon there's the "Colorado Provençal" near Apt, you want to get a ride in there for the scenery. Some marked loops, but none of them all that exciting, IIRC. The terrain between Apt and the Luberon is great for trailriding (and there is some tech stuff), but the good stuff is not so easy to find. Best to ride with a guide. Gaetan Dupin is a guide in the Apt/Luberon area, nice guy, could also give you the adresses of a few more guides. Google "gaetan dupin vtt".
I found some loops on the Luberon on the net (can't remember where), but only one had a good descent. I could look that one up on a map, if you're interested.
Between Avignon and Nice, you've got Digne-les-Bains. Never ridden there personally, but Bruno Chabalier who works as a guide there is a great guy and sure to show you the good stuff (brunochabalier.com).
About 100km west of Avignon you've got the Haut Luberon range. Try finding someone to guide you there by contacting Velo Caroux (http://velo-caroux.fr/en/group), they can also help you with accomodation and rent bikes. The two rides I did with them rank among the best in my life. Awesome trails in a rugged landscape with relatively few tourists.
Be warned: If you're alone, hiring a guide can be pretty expensive, as they now usually have a minimum price for an outing (which you could split as a group).
A bit east of Nice there's Finale Ligure in Italy. A must, apparently, everybody who's been there was blown away. Trails, guides, shuttles and rentals aplenty. Haven't been there myself yet.
There's plenty more good riding in that area, but that's the stuff I know.