For the Cote d'Azur, try
Holiday Bikes, its very close to Les Promenades d'Anglais. To do the circuit you're implying, you would have to take the highway, which is two lanes.
For the Vaucluse, hilltop villages are just that, on the top of big hills so expect it to be steep. However, it's definitely not the steepist there is in France. There is limited but fuctioning bus services in all around the region.