The song itself is called
Laetamini in Domino. The text (in a Gregorian chant version) is the offertory antiphon assigned for Mass at a feast of two or more martyrs in Paschal time, and on the feast of Sts. Fabian and Sebastian on January 20. (Really, it has no place as a processional hymn.) The words are Ps. 32 (31):11,
Laetamini in Domino, et exsultate justi: et gloriamini omnes recti corde.
Be glad in the Lord, and rejoice, ye just, and glory, all ye right of heart.
This offertory has been set to music by a number of composers, including Palestrina; I thought
this setting by Richafort was cool. Unfortunately, I’m not familiar with the version in your video, and poking around for a bit I couldn’t find it. Maybe you’ll have better luck, but it’s very possible it’s just entirely unfamous and not findable. I’m pretty sure it was not composed just for the movie.
P.S.: yeah, jbuck, that choir is
terrible! They warble like a bunch of old ladies – and need a reedy organ to back them up. I’ve got no doubt that it
is very authentic, because in fact Catholic music 100 years ago was, by general consensus, pretty awful.