That 's right! "Tu es" in latin is exactly the same with "tu es" in french, but it is pronounced differently.

As I know, western European languages derived from latin, especially Italian, French, Spanish, Portoguese and Romanian. This is what I was taught. Even English has many many words that derive from latin and ancient Greek of course. But these languages were not entirely evolved from Latin. They are a mix of latin, dialects of each country and "barbarian" languages as αναγνωστης has mentioned. Therefore, we cannot consider them as a natural evolution of latin, in the way modern Greek is a natural evolution of ancient Greek. I think you can find some books that can explain in depth all these.

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In Vatican, Latin is still the official language of the government and all documents are written in Latin. Personally, I don't know whether this language can be considered as modern latin. And of course latin is still the language of the Catholic Church.