Now, it is a late piece, 14th century, and really doesn't qualify as Gregorian at all except in the broadest sense of that term: Latin plainchant. Still, it partakes so well of a liturgical sense even while it has both popular flair and an antiphon that anyone can sing.
It is Resonet in laudibus. Here is a clean copy.
The song has seven verses that sing of the newborn King.
Let Zion resound in praises with the joyful acclaim of the faithful:
R. He whom Mary bore has appeared. Rejoice, rejoice, Christ is born today!
Rejoice, rejoice, born of the Virgin Mary.
2. Zion, laud your Lord, Savior of all, Son born of the Virgin. 3. Gather round,
ye children; sing to the newborn King with a voice of piety. 4. Emmanuel is
born, whom Gabriel prophesied and Ezekiel testified. 8. O Juda, with the
singers go out the gate and sing with the shepherds. 6. Who reigns in heaven,
has come to seek the sheep, not wishing their ruin. 7. To Thee, Holy Trinity,
may high thanksgivings ring out from all lips.
The melody is as charming as any I've ever heard with just enough that is different from today's popular music to signal that it is something different from other song. I don't see any reason why this hymn couldn't be used following communion or anytime. There are a zillion choral arrangements online but no plainchant that I can find. And yes, I've tried it in three and its nobility is lost in that pattern, so my instinct says: keep it as written.
The Latin is easy and builds confidence on part of the schola, which can sing the verses, and the congregation, which can sing the refrain. It also has a way of staying with you, and I can easily imagine that it would become a parish favorite for Christmastide.
