While I was listening, I heard him pronounce [h] in the word "haine," 1:55 into the clip. I checked another singer, and Luce Dufault does the same (2:30).
It's tempting to say that it's a Québécois thing, but I have never heard the h aspiré actually pronounced by Québécois. So I'm guessing it's a singer thing. What do you guys think?