Map excerpted from the article Austrasia on Wikipedia

The fall of Rome in the West affected more than just the city of Rome and the Italians; control of Roman Gaul devolved to regional kingdoms. The map above shows Gaul after the Romans decamped, a world your teachers glossed over in the rush from the Romans to Charlemagne. Mine did, anyway. And if you look closely (notice the map key), it also shows the extent and episodes of the Carolingian conquest.