The solution to the accomodation problem in France (and most of the rest of Europe) during July and August is to camp - If you are cycling, even the most crowded camp site will find somewhere to put a cyclist with a small hike tent
There is a Lonley Planet book called something like Cycling in France - It's totally useless for routes, but its great for general info, bit's of the bike in French, how to pack a pike, rules (both written and unwritten) of the road, and general stuff on France
Read the book before you go and then leave it behind as it weighs about 1kg