We did a holiday in this area last May. TGV to Nimes, then Avignon, Marseilles, Aix-en-Provence and back to Paris. The trains between places are reliable and cheap, but with small children your needs will be quite different from ours (mine are all grown up). Your idea of staying in one place is probably a good one; Nimes is lovely and has a huge park with fountains, ideal for children who are tired of sightseeing, also has good train connections. - probably best to avoid the bull fighting fiesta though! PM me if you have further questions.