The reference to the song in France that I found is in a program given by the Wheaton College choirs, and thus may be unrelaible. The program song introduction has this note, presumably by a professor at the College.

"This song has been well known in some French provinces since at least the 1880's. The text appears, at times, to be nonsensical due ttto its "game of rhymes" in which the final syllables of each line all rhyme* with the 'tends of "J'entends." The arrangement used was commissioned from Donald Patriquin, lecturer at McGill University in Montreal, 1992.
* the Patriquin arrangement differs from the one I quoted. From the program:

J'entends le moulin tique tique taque
Mon pere a fait batir maison.
L'a fait batir a trois pignons.
Sont trois charpentiers qui la font.
La plus jeune c'est mon mignon.
Qu'apportes-tu dans ton jupon?
C'est un patee de trois pignons.
Assseyons-nous et le mangeons.
En s'asseyant il fit un bond,
Qui fait trembler mer et poissons,
Et les cailloux qui sont au fond.

A translation also is on the program:

I hear the mill tique tique taque
My father is having a house built.
It is being built with three gables.
There are three carpenters building it.
The youngest is my darling.
What do you have in your apron?
It's a pie made of three pigeons.
Let's sit down and eat it.
While sitting down they all leapt up,
Causing the sea and fish to tremble,
And the stones on the bottom of the sea.

Several websites offer the Patriquin sheet music, but I haven't checked them to see if his lyrics are available.