The music to "Non nobis domine" used in the Henry V movie was composed by the 16th c. English composer, William Byrd (1543-1623).
With corrected spelling-

Non nobis domine, domine
non nobis domine,
Sed nomini, sed nomini,
tuo da gloriam.

There is speculation, but no evidence, that the piece was composed for the Shakespeare play.

The Church uses these words:
Non nobis domine, non nobis,
Sed nomini tuo da gloriam,
Sed nomini tuo da gloriam.

The full Mouton text and translation is here: Non nobis domine