LaurieDi,
If you are not thinking of the Riviera area, but do want some coast, I would recommend some time in Bandol, just about an hour east of Marseille. It has a lovely harbor, some sand beaches (and others nearby as well), access to wineries (especially for some great roses, but Cotes de Rhone and others), a nice-sized typical street market on Tuesdays, and a lovely overall Mediterranean ambience. It is less than an hour's drive to/from Aix-en-Provence, and 1 1/2 hours to/from St Remy de Provence, really close to many charming towns in the region that are worth at least a day's visit. And a day trip to Marseille can be a treat to enjoy some terrific bouillabaisse and a visit to the Vieux Port, Notre Dame de la Garde, Chateau d'If, a boat ride to the calanques, the Museum of European and Mediterranean Civilasations.....lots to see and do there.
By train from the Gare de Lyon you can take a TGV to Avignon or Aix-en-Provence or Marseille, and you can rent a car at their train stations (a car is really recommended in order to see a lot). Driving out of Marseille isn't fun, so you may opt to take a train to Aix. Car rental options at Aix may be limited, but there are frequent buses to Marseille airport where there will be a much bigger selection. And you would avoid driving to or from Gare St. Charles (the train station) The bus ride is only a half hour.
The "south of France" encompasses a lot. IMO most Americans think of the Riviera when they say "the south of France", but the whole coastline, from Italy to Spain is about 675 miles long. And the "south" goes inland for some ways, up to the Drome or Basses Alps areas, even the Dordogne is considered to be in the south of France. You might take a look at a full paper map of the area of southern France. In the western part of southern France are Montpellier, Collioure, Gordes, Carcassonne, Bordeaux, Narbonne, St. Tropez....... a wealth of choices!
Whatever you choose, based on what you envision your trip to be, you will have a wonderful time!
Amusez-vous bien!