The Mont-Dore area of the Auvergne is home to glorious volcano landscapes that are wonderful for road cycling.
Cycle tourism based on road riding is not as developed in the Mont-Dore area as it is in many other regions of France - which means it really is possible to head out and have the the roads to yourself. This area is better developed for mountain biking, but there are some seriously good road routes if you know where to start.
In this area you'll find the Col de Guéry, Col de la Croix Morand, Col de Croix Saint Robert and La Stèle, while a little more farther afield are Banne d'Ordanche, Col de Vendeix and the Col de la Sœur. See here for more on local cols. Then, of course, there is the Puy de Dôme, which unfortunately is closed to cyclists except on special occasions (this is the website to watch for dates).
Click the routes on the map above for a taster. Each route starts at the bike-friendly Les Camelias, whose owner (hi Margriet!) has charted them for us. There are several variations in both mileage and difficulty for each route, so drop either Margriet or I a line if you'd like them all).