This is true. French is the most "Germanic" of the Latin languages, for historical reasons (and no, I'm not talking about the bad WWII jokes). The Franks were germanic tribes and did influence the Latin spoken in Gaul. Also, more recently, don't forget the shared history of Britain and France when they shared the same monarchs (Normans and all that stuff). French influenced English a lot, and vice versa. Also, modern French is the dialect which was spoken in Paris (langue d'o?l) because it was the language of kings and official documents and such, which had more Germanic influence than langue d'Oc which was spoken in Southern France.
I know I'm simplying a bit but that's the jist of it.
Do note that today's French has more vocabulary in common with English than with any other language (Spanish, Italian, etc.).
True enough. There have been multiple instances or waves of French influence on the English vocabulary. I can't think offhand of any examples deriving from the Norman invasion (which would have influenced the upper class more than the main body of English society) but certainly more modern examples include words like
apartment, department, bureau and the like, which are pretty much straight cognates with their French equivalents, and which largely are no more than about two centuries old or so, at least in terms of English.
What kills me is that the modern French - at least the Academy - is so paranoid about the inclusion of foreign words into modern French. They take this to the point of trying to get people to adopt "French" alternatives to foreign words like "computer" and "email" and the like. People still accept the foreign words in everyday conversation, of course, but if I'm remembering right, there might be some laws against these sorts of words finding their way into official legal documents, advertising, and so forth. Utterly mystifying.