Latin was the primary spoken and written language of the Gallo-Romans. It existed in its classical form but also in a myriad of regional, low Latin forms - essentially local Latin dialects.Prior to the barbarian "invasions," I do not know what colloquial languages were common among the Gallo-Romans. Maybe someone on here does.
The ancestors of languages such as Basque seem to ave existed in the south of what is now France.
There is a big debate amongst French academics as to whether or not Gaulish survived into the post-Roman period. Gaulish was a Celtic language related to British, the ancestor of modern Welsh, Cornish et al. Some believe that modern Breton is a development of Gaulish, others that Gaulish had died out during the Roman period and the Breton language was an import from post-Roman Britain.