Can you ever learn to speak a foreign language as a native does?

As some of you know, I am wrestling with the French language weekly. There are billions of rules but there seem to be even more exceptions to the rules. (And why countries, states and cities need to have gender, I’ll never understand.) In addition, there are always the little expressions and idioms that one just hasn’t learned.

So I’m wondering, even if one lives in a foreign country for some years, would one still be able to speak exactly as a native does or would there be certain “tells” that would expose you as a non-native speaker?