Apparently my knowledge of French pronunciation is nowhere near sufficient to figure this out. Based on the Wikipedia article, it seems the first line is supposed to sound like “Humpty Dumpty.”
I speak French, and did not immediately recognize "Un petit d'un petit" as "Humpty Dumpty"; the "correct" reading relies on knowing that a native French-speaker might pronounce "hump" as "ump". It is not simply a mapping of syllables to phonemes.
In other words, it's an extremely targeted joke, intended at people who have specific expectations about how both French and English are read and spoken.
Eh, did you notice there's no h in 'ere?
It's 'cos they left it in h'Ottawa.
Another joke we have refers to how the French pronounce the English word "happiness."