I know the current language spoken in the area we call France is a Romance language, but why is it Latin based? Latin obviously wasn't the predominant language before the Romans came, and according to Wikipedia wasn't the predominant language during their rule either, though popular among the elites. From what I gather most of the the people in the area would have spoken a Celtic or Germanic language, Frankish or Gaulish during this time, as well as the centuries after. Charlemagne comes along and sort of united the region, he and his peers were elites so would have known Latin. His lands split into successor states. The people now in France speak a Romance language. The people in Germany speak Germanic.
I assume the elites who ruled after Charlemagne would have spoken whatever Charlemagne spoke, especially with each other. I could understand if the West and East developed different variations of the same language root, but French and German don't even have that. And both ruled over Celtic and Germanic people.
It seems to go from no Latin, a bit of Latin under the Romans, a bit of Latin after the Romans, then a bit under Charlemagne, all over that part of Europe. But a Latin based language develops in the Western/France part, but not the Eastern/Germany part. The ruling class of both were from the same family, and the people they ruled had similar languages. Am I assuming something really wrong, is this just a quirk of history, or something else I'm missing?
More can be said about it, but you might be interested on these previous answer
In short, Latin was not only the prestige language in Gaul but became widely spoken by the population as a whole, and not just the elites, due to early and sustained romanisation/latinisation of the provincial societies : as they did so, with significant political (local, regional or imperial) support, the language "rippled down" to countryside population no later than the IIInd century.
While Gaulish might have been still spoken up to the VIth century, it was in all likeness no longer widely so : for instance, all Gaulish words in modern romance languages, passed trough Latin and not directly to them, implying that Celtic substrate played little influence into the formation of these language.
Franks, as other Germans, were also importantly romanized and either became heavily latinized once settling in Gaul or were actually descending from Romans assuming a Frankish identity.
This previous answer from u/clovis227 addresses the earlier part of your question on the spread of Latin in the area of modern France.