Most of my life, especially when I was catholic, I thought that the line from the Christmas carol came from Jerome's Latin Vulgate.

And for a while, after I was saved, I still thought the same thing.

However, I was shown that phrase, "Gloria in excelsis Deo", comes from the Vetus Latina, the old latin Bible, before the Vulgate.

Interestingly enough, this is presented clearly on a web page called, "Vetus Latina facts for kids":

Vetus Latina facts for kids

Vetus Latina is the name given to a collection of Biblical texts that were translated into Latin before the Vulgate became the standard version used in the Latin-speaking world. The texts themselves are written in Late Latin, not in Old Latin. They often use different words than the Vulgate. No complete manuscript survives, only fragments are known. Many text passages are known because Church fathers such as Augustine of Hippo cited from them.

Since the Council of Trent, held in the 16th century, the Vulgate is the official Bible translation for the Roman Catholic Church.

Some of the Vetus Latin texts survives in the Liturgy, however:

Vetus Latina	Latin Vulgate
Gloria in excelsis Deo, et in terra pax hominibus bonae voluntatis	Gloria in altissimis Deo, et in terra pax in hominibus bonæ voluntatis

The Old Latin text means, "Glory [belongs] to God among the high, and peace [belongs] to men of good will on earth". The Vulgate text means "Glory [belongs] to God among the most high and peace among men of good will on earth".

Probably the best known difference between the Old Latin and the Vulgate is in the Pater Noster, where the phrase from the Vetus Latina, quotidianum panem, "daily bread", becomes supersubstantialem panem, "supersubstantial bread" in the Vulgate.