A Lizard (poetry or nursery rhyme)

Hello everyone,

I'm looking for a poem or maybe a nursery rhyme, but I'm leaning more towards a poem, where the word "Lizard" appears several times. The title might be "A Lizard" or "The Lizard," but the poems I've found online with those titles don't match what I'm looking for. And I can't remember the text, nor the name of the poet.

I know it's a poem that some elementary school students (around CE1/CE2/CM1) learned in the 60s/70s when they were about 7 or 8 years old, or maybe in middle school, so a little older. Therefore, the text (vocabulary) must have been quite simple and surely short enough for children of that age to understand and learn.

I also know that it's not the poem by R. Desnos, nor that of J. Prévert, nor that of A. De Lamartine.

Since the text is in French (I believe it’s the original text), I imagine that the author of the poem was French or Francophone, but I don't know when it was written.

Do you have any ideas about who the author of this poem might be and especially which poem it is?

Thank you in advance.