If it’s the origins of specifically the 5,000 most frequent words in the English language that you’re interested in, that’s fine. But that simply doesn’t have any relevance to the question of how English should be classified, according to the conventional definition in linguistics. I stress again that this is a conventional definition. You can come up with a classification system that will group English with French to the exclusion of German, if you like; it just won’t be the same as the conventional one which linguists are familiar. So you could, if you wanted to, use your data to argue for English being grouped with French. But you’d have to create and justify a new classification system. And either way, the statement that “English is more French than we thought” (if “we” is taken to refer to linguists) will be misleading. In stating that English is more closely to related to German than French, linguists have not been implying that most of the 5,000 most frequent words in English are of Old English origin.
You display some signs of being confused about the subjectivity of definitions: talking about which definition of “core vocabulary” is the most “accurate”, presenting your choice of not weighting words by frequency as the straightforwardly preferable one, etc. A definition is a tool that you use to talk about real things. You should always think carefully about what real stuff you’re saying when you use a definition. And crucially, you should always think carefully about what real stuff *other people* are saying when *they* use a definition.