File under “not so easy to google”, along with !!!. -M- (his more retrievable given name is Matthieu Chedid) hails from a musical French family, and created his on-stage persona to combat his natural shyness. Wikipedia tells us:

The character ‑M- is a superhero, noted for having a playful nature, and recognized for his flamboyant costumes (primarily monochrome suits with slim trousers and long jackets with upward pointed collars) and hair styled into the shape of an M.

It’s a little hard to reconcile that description with what is a pretty laid back track, sung in a not particularly flamboyant style, so I guess - M- himself has an alter ego he brings out for the straightforward classic soft rock moments like Ma mélodie.