Thanks a lot! No, nursery rhymes were not obvious to me at all as I don't know any French ones - therefore I appreciate your explanations. I still don't understand the overall meaning of the song except that it is meant to be funny. I find it puzzlingly funny [I use non-yet-existing words because English just doesn't have enough to convey my sense of humour].
At least Le Rat has unclear but coherent narrative - ever since I started translating songs I have discovered that most of them stripped from music make no sense whatsoever.
Best regards,
Some references to nursery rhymes are obvious, but I may have missed a couple more, awash in a flood of delirium...