I've spent some time in St. Jean de Maurienne, I'd second all he says. The Glandon is a fantastic decent. Riding the lacets and then traversing over and hitting the Madeleine part way up is really nice too. I prefer secondary white roads over the major passes, there're usually narrow, empty and the tarmac is good.+1 to all of the above. St. Jean de Maurienne is the place to base out of for a bunch of climbs like the Madeleine, Croix de Fer, Glandon, Galibier, Lacets de Mont Vernier etc. More of an industrial town than a tourist hotbed, but well located. If you're keen on the other side of the Galibier, Izoard, Lautaret, Les Deux Alpes, Alpe d'Huez, etc. La Grave is the place to stay.
The Tourmalet and surrounding passes are great as well. Hard to go wrong in the Alps.
Mt. Ventoux if you are close. There are 3 different routes up. All the famous Alps climbs are great. I have never been over to the Pyrenees.
Check out climbbybike.com and you can get profiles of all the climbs in whatever area you are going to.
Also, France closes off car traffic on most of the famous climbs for one day during the summer. You should be able to find the schedule for each hill online. Thousands of riders usually show up on these days, great fun.