If P = NP, then is NP = FNP?
No, it doesn't mean that FNP = NP.  NP is a class of decision problems; FNP is a class of function problems.  See the definition of FNP (e.g., on Wikipedia, or in any textbook).  Therefore, the elements of NP have a different type than the elements of FNP.

It's like asking whether the set of tart apples is equal to the set of seedless oranges; one is a set of apples, the other is a set of oranges, so they're certainly not equal, and you don't need to know anything about exactly which apples are tart or which oranges are seedless to know that.