I seriously suck at nursery rhymes - as in that I don't know any of them.
Luckily, in 2011 we have this very awesome thing called YouTube, which lead me to this video
I remember singing this a lot a few years back as it gets stuck in your head, though I always thought it was about a clock personally. But according to YouTube it is about a bird who gets all of its appendages plucked off one by one. How rather disturbing, but totally addictive. Maybe I just won't teach our child French and they will never know.