I don't see an anti-rattle spring as one of my calliper components :
I had a look and there was a missing shim on one of the brake pad. I stole one from the other wheel to see if the noise would stop but it's still there.
Actually, I realized that I could ear it just by swinging the car while it's parked. So I asked a friend to swing it and I put my hand on the inner CV joint boot and I could feel something wrong in there when the noise is heard.
So is it possible to have a broken cv joint that wouldn't make noise while turning ?