The Gauls descended from at least two groups: Celts who were living in what is now eastern France by about 600 BC, and presumably non-Indo-European native populations, about whom we know very little.

As the Celts moved into the rest of Gaul, they intermingled and interbred with the native populations. The replacement of earlier languages by Celtic-based Gaulish by Caesar's time indicates that, as in Britain, the Celts had achieved social and political domination over the area.

All the people we're talking about lived in tribal rather than national societies, so Celtic "invasions" could not have been military operations decreed by a central government. They resulted instead from   tribal migrations in search of new territories. Local levels of violence depended on the degree of resistance of the locals, which presumably varied.