French is a daughter of Latin, so it's safe to say its vocabulary is inherited from Latin. Or ist it? Basic vocabulary items such chien, chat, eau, feu can be considered as inherited as they are, well, basic, and also have undergone dramatic changes regarding forms and pronunciations. Some items are obviously (or are they?) borrowed directly Latin, such as anus, cactus, etc. as they never underwent any significant modifications. Some items such as impératrice, in-, Amérique appear to be kind of middle ground, as they were introduced more recently and underwent only minor nativization (compare empereur, en- which underwent more notable changes).
So my question is: What are the criteria for the "inheritedness" of a word derived from Latin? In other words, how can we determine if a word is inherited from Latin, or just a mere borrowing from Latin?