I tend to sing it as if I'm singing Frere Jacques with the doubling taken out, with extra repeats to cover the peeps, which makes it extra craze-inducing.

i.e.

   Fre-  re    Jac- ques / Dor-mez vous?
A thou-sand eggs all / nice and warm

Son-nez les  ma-TI-nes   /      Din,      Din,    Don
Pe-EP  peep peep PE-ep! / another, chick is, born

Son-nez les  ma-TI-nes   /      Din,      Din,    Don
Pe-EP  peep peep PE-ep! / peep-peep, PEEP, PEEP


                     Fre-          re    Jac-ques /Dor-mez vous?
Nine hundred and ninety nine eggs all / nice and warm

...

:D