Those Gaulish, Germanic and Celtic elements were becoming Romans as a result of them starting speaking Latin/the Vulgata, the same goes for all the peoples living at the periphery of the Empire. If you were still speaking Celt/German or whatever you were not a Roman, you were a barbarian.

In the Italian peninsula the only part where Greek might have still been a thing is of course Magna Grecia, but that’s a special case. Curious of how many Greek graffitis have been discovered in Pompeii.