Normally before a word beginning with a vowel, a nasalized vowel at the end of a word loses its nasalization and the final "n" is pronounced as if it were the 1st letter of the next word.
"Divin enfant" pronounced "divi-nenfant" is the only case in which the "i" from "-vin" recovers its original sound -the 4 other existing cases (Achille, Homère, Ulysse, amour) are seldom used if at all and derive from this one. There's no grammatical/phonetical explanation. It's just been spread this way from the beginning. It was published in 1874 for the first time. Here is the original score with no lyrics (#8 at the bottom of the page).