This question is mainly in reference to the Franks, Ostrogoths, and Visigoths, who took control of France, Italy, and Iberia in the fifth century CE. While the native Romance-speaking elite did manage to hold onto a considerable amount of its wealth and influence, all of the rulers in the early Middle Ages seem to have been members of Germanc tribes that had moved in. Presumably in the early years they spoke their respective Germanic dialects, and if I recall my reading, Charlemagne in the late 700s still spoke Franconian as his native language and not proto-French.
How and when did the rulers of these places change over to speaking only the Romance languages then current among the general population? It’s interesting that in the Mediterranean countries, the native language of the conquered inhabitants won out, while in England, the Germanic language of the invaders won out. Interestingly, the process of language substitution was repeated in Normandy in the 800s, when William the Conqueror’s Danish forbear received the region in fee from the French king, who was himself not so far distant from his Germanic speaking ancestors. Yet by William’s time, nobody in Normandy appears to have been speaking Danish anymore.