Spanish here. Got an estimated vocabulary size of 17,7000 words. I lived and worked in the U.K for a couple of years. I think I might be in a better position than some of you when it comes to words derivated from Latin, as they are almost always the same in Spanish. Leaving those out I am sure I would get similar results.
French here, and I concur. Quite a few terms are directly borrowed from French or have very clear Latin roots, making them easy to understand even without having actually encountered them in English.