That reminded me of her appearance on this show with Garou where she sang "Sous le vent". It was a song he sang in a duet with Celine Dion and on this show, I believe he was supposed to take over half way through, in fact you can see he was holding the mike up to his mouth, but for what ever reason, she kept going by herself, maybe because she was doing such a good job with it.
Below that is the Les Enfoires performance Alizée must've been refering to when she talked about looking into Garou's eyes. The interview was from April 2002 and the "Aimer" video was a couple of months before during the Les Enfoires show.