This is all digression, since Margaret V was looking for a cd with French carols sung by children. Except for a couple of apparently out-of-print recordings, we have struck out.

Like many other old songs, attributions include hearsay, errors and speculation about origins. The carol "Orientis partibus adventavit asinus" has a tune attributed to it that is the same as that of the carol sung in English as "The Friendly Beasts."

If you read the information at the link given below, it becomes evident that the words were written by Robert Davis (possibly based on an older English source).
The tune "Orientus partibus" was modified by Richard Redhead in the 19th c. and brought to its current state by Ralph Vaughan Williams (English Hymnal, 1906). Put together, this is one version of the present carol.

Donkey or Beasts

In other words, we have an English carol partly based on an old Latin text that some believe dates to the 12th c and may have been written by a Bishop in Sens. The "French" attribution,to be charitable, is a gross oversimplification.
The Germans also took the Latin carol and have reworked it as a German carol. It achieved some popularity there, but it never seems to have become popular in France as a "French" carol.