This is known to history as the Barbarian Invasions:

31 December 406 is the often-repeated date of the crossing of the Rhine by a mixed group of barbarians that included Vandals, Alans and Suebi. The Rhine-crossing transgressed one of the Late Empire’s most secure limines or boundaries, a climactic moment in the decline of the Roman Empire that initiated a wave of destruction of Roman cities and the collapse of Roman civic order in northern Gaul.

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