It would be very hard for a Germanic language to replace Latin as the Lingua Franca so early on, almost impossible even. Most of the peoples that the Germans conquered were full of Roman citizens that spoke Latin, especially the upper class scholars, scribes, and priests that they had to rely on. Not to mention that states like the Carolingian Empire or the HRE prided themselves on being a successor to the old Roman Empire in some form or another, so inevitably they would use Latin in some upper level capacity.
In later periods, I believe that it would be more likely, as I think a German-dominated Europe like a HRE wank could lead to German replacing French or Spanish as the lingua franca during the Late Middle Ages or the Early Modern Period, but I can't say for sure.