Traveling around the South of France with no car.

The coast around Nice is well served by both bus and train. Some smaller inland Provencal sites can also be reached by bus, such as from Avigon, Nimes, or Nice. Rick's Provence and French Riviera guidebook provides pretty detailed transport summaries for all the towns he covers, and covers more southern destinations than does his general France book.

How to Look Up Train Schedules and Routes Online gives you the DB train schedule link and tips for using it. (One route that is not on there is Nice-Digne by http://trainprovence.com/.)

Since bus companies vary by region, you can find them through Google searches, or www.rome2rio.com, or Tourist Information Offices, both online and in person as you go.

To buy the Paris-south train ticket at the best price, book early, preferably about 3 months ahead.

In Provence, Arles is probably the most central location with good connections to the rail network
Nimes and Montpellier are west.
Avignon and Orange are north.
Aix-en-Provence and Marseille are south east.
On the Riviera Nice is the largest and most central location.
Monte Carlo and Italy one way, Cannes and Antibes the other.

The best way to find bus information for rural parts of France, if you can't find a town bus network, is to find out the name of the departement that the location is in, then do a web search for the departement name and "transports en commun". The websites are very rarely available in English, though, even in heavily touristed regions.