I spent two weeks in the Luberon area a number of years ago camping with my family and some friends (travelling by car) and as noted, there are all kinds of neat areas to explore.
I cant help with specific biking routes, but as axo says about the heat in May, I was there in August and would absolutely NOT recommend biking there in Aug as it was oppressively hot (many days of 42-43c) and could not imagine biking. These were days when even at 9-10 pm it was still over 30c.

Check out the web for avereage temps for a given town, you should be able to find reliable sources that will give you an idea for a given month.