It was probably inevitable that a married couple of songwriters named Noël and Gloria would write a Christmas song. Noël Regney and Gloria Shayne wrote Do you hear what I hear? (first recording, by the Harry Simeone Chorale) in October 1962.
Or maybe not, because his name was actually Léon, and he was hesitant to write a Christmas song due to the commercialisation of Christmas. Noël wrote the words, influenced by the then-current Cuban Missile Crisis and Gloria the music.
Gloria came into English straight from Latin, and also via Old French glorie to become Middle English glory. I couldn’t figure out what the origin of noël (or noel) might be, and would not have guessed that it comes from Latin diēs nātālis day of birth (compare nativity). French did drastic things to Latin (note also that glorie became gloire), but that one is a stretch. Noël is a relatively late arrival into English, dating from 1805-1815. The First Nowell was first published in 1823.