I've toured a few times in France, and agree with almost everything that's been said. For someone from the UK (like me) France is a BIG country, and you shouldn't expect to explore all of it in two weeks. So maybe consider the Pyrenees but not the Alps, for example. Plenty of lovely lowland riding in the South of France too - for a really easy ride you could follow the Canal du Midi from Carcassonne eastwards towards Beziers, then head south-west into the mountains. Provence is lovely too, but beware the Mistral! Mont Ventoux is kinda iconic, especially for Brits (on account of Tommy Simpson). I must ride up it one day - Iban Mayo did it in 56 minutes, so I'll need about four hours!
Using trains is possible in rural France, though not always as easy as in German-speaking countries, which are VERY bike-friendly. But if you check the timetables carefully, you should be able to leap-frog some of the less interesting regions. Good maps are important, as signage in rural areas, even on motor roads, can be poor. Be aware that many French people take most of August as their annual holiday, so shops and restaurants, especially ones off the beaten track, may be closed. When you do find food, it will be excellent, of course - but stick to "official" mealtimes (generally 12 till 2 for lunch, 7.30 till late for dinner) and don't expect to find much in the way of "real" food outside those times, except in bigger towns (or hypermarkets, or motorway service areas).