I was thinking of "Noe, noe, noe, psallite noe" by Jean Mouton, 1519.

When searching for "Allons...", also try without an s on "Allons", and with only one "gay". Four permutations in all. I have no precise year, but Costeley's dates are 1531-1606.

"Psallite unigenito" is in the New Oxford Book of Carols. You can also find it at the Hymns and Carols of Christmas site (flick).

Another nice one is "Omnis mundus jocundetur" (or iucundetur), also by Praetorius, Musae Sioniae, 1607. It's in the NOBoC, though they've revised it in some gratuitous ways. John Rutter wrote a set of English words: "Earth this glad day rejoices." Well, mostly English; he has three lines of the refrain in Latin, but curiously, not the same Latin as in Praetorius's text.