I'll quote Procopius, a 6th CE source:

"Now other Roman soldiers, also, had been stationed at the frontiers of Gaul to serve as guards. And these soldiers, having no means of returning to Rome, and at the same time being unwilling to yield to their enemy who were Arians, gave themselves, together with their military standards and the land which they had long been guarding for the Romans, to the Arborychi and Germans; and they handed down to their offspring all the customs of their fathers, which were thus preserved, and this people has held them in sufficient reverence to guard them even up to my time. For even at the present day they are clearly recognized as belonging to the legions to which they were assigned when they served in ancient times, and they always carry their own standards when they enter battle, and always follow the customs of their fathers. And they preserve the dress of the Romans in every particular, even as regards their shoes."

Also keep in mind many Germans had served in the Roman army and could have returned to their tribes with all their training so some of Rome's military traditions would have passed on into the successor kingdoms.

Also the Roman empire in the east didn't fall until Constantinople was conquered by the Turks in 1453 CE and despite all that time removed the Byzantines still considered themselves "Romans" (though they don't look as such to us).