In a Google Books search snippet of a book from ca. 1936 on the Comédie Française, the title of the carol was listed with several others. Elsewhere, I found it in a list of carols whose dates had not been determined, in close proximity to some of the same carols, but here it was titled "Ture-lure-lure, en marchant à l'étable".

I have a suspicion that this song may turn out to be a variant of "Ture-lure-lure, lo gau canta/le coq chante", a carol collected by Micolau Saboly, because the other carols in the mentioned lists turn up in similar proximity to it in other mentions. Admittedly, "ture-lure-lure" is just a French form of mouth-music, like "tra la la", common to many songs, but I haven't encountered other French carols which use it, despite the dance origins of most early carols. Curiously, the title which followed "En marchant" in the first list I found was "Turelurelure déjà tinte", which shows that there are other carols which turluter--not entirely surprising, considering the dance origins of carols.