If the Wikipedia entry in the OP is correct, then the vowel in Monfils is the same as that in the word haughty, except nasalized. (The tilde over the vowel in the Wiki entry indicates nasalization.) The easiest way for an American English speaker to think of it might be to imagine it halfway between maw and mong, in which the final sound is pronounced as in sing. The trick is to pretend the nasalizing consonant (in Monfils, the /n/) is still present, even though it is actually silent.
And as several poters have noted, mon fils means "my son." (I've always called him "The Priest" for this reason.)
/linguist
//yes, very cunning