@blueemu Not familiar with FIDE, but I will bite, Black. No illegal move was made. The move put white in check. Whites move must be to first to get out of check which he cannot. Mate. Or is this a trick question perhaps based off of old FIDE rule which has been updated?
You are correct, Black wins.
The simplest way to refute White's outlandish claim is to point out that his statement "Your Pawn never reached the d5 square" is false. Official FIDE rules make it quite clear that a move is completed when you move the piece and take your hand off it. The rules say nothing about "not actually complete until the opponent decides whether he wants to en passent or not".
So Black's Pawn DID reach the d5 square, blocking the check. So it is White, not Black who is mated.
@blueemu Not familiar with FIDE, but I will bite, Black. No illegal move was made. The move put white in check. Whites move must be to first to get out of check which he cannot. Mate. Or is this a trick question perhaps based off of old FIDE rule which has been updated?