Of course there have been mass population movements. We remember how in the later years of the Roman Empire many peoples quit their homes on the steppes, the Caucasus or the forests of Germany etc. and sought pastures new in what is now France, Spain, Italy and Britain. Thus France for example, though loosely coterminous with what was once the Roman province of Gaul, is the Kingdom of the Franks.
Did they move en masse, or did they leave some of their population behind? It may vary from case to case. There are still Saxons in Germany, (and Romania, oddly enough) though a great many Saxons migrated to what is now England. On the other hand, there are no known Franks anywhere except France.
One well-documented case is the movement of the Helvetii, famously recorded by Caesar in his publicity. According to him at least, they did attempt to move their entire population from the chilly climes of what is now roughly Switzerland into the warmth of Roman-ruled Gaul. (IIRC, they were prompted by a harvest failure. No foreign aid in Roman times.)
Caesar came down on their wagon trains of course. And many of the survivors did return to their former territory. So it isn’t an example of mass population transfer being done successfully. If Gaul hadn’t been under Roman rule though - or if they’d had a less efficient general than Caesar - it might well have succeeded.
An interesting aside though: The numbers Caesar gives for the Helvetii whom he killed and who returned to Switzerland add up to several thousand less than invaded Gaul originally, so it appears that some did escape to settle somewhere. One - wildly speculative! - theory advanced is that they reappeared as the Gael, the Celtic people who gave the Gaelic language to Ireland. It would explain why Gaelic (Irish) is a Q-Celtic language, otherwise only known to have existed in central Europe, as opposed to the P-Celtic languages spoken in neighboring Gaul, Britain, and indeed in Ireland before that.
(It’s a fun idea and it’s just about within the bounds of possibility, but it seems more likely that the Gael arrived in Ireland a couple of centuries before that. Alas the ancient Celts generally mistrusted writing and preferred to transfer their records by memorization, so there is very little solid evidence that predates Christianity.)
