From now on till end of october you can ride bike in every plain regions in France. In summer, the weather is usually very hot in Provence. If you want to visit France and find accommodation easy, I should recommend september or june. I live in Limoges, I confirm that there are a lot of nice little roads to ride. But the weather may be very changing. You can also prefer more touristic areas such as Loire valley, Perigord, Brittany, or Provence.
I think you will find the best maps of french roads on this website :
http://www.viamichelin.co.uk/