The Film is called "Eversmile New Jersey".It is set in Argentina, and according to the blurb I have just read, the dentist is supposed to be American, though I'm sure I remember him being Irish.
Anyway, he does (if I am remembering it correctly) sing a gaelic version of "she moved ..."
A-ha ... I've just had another look, and the name of the character is Fergus O'Connel. Seems likely to me that the character is Irish. hmmmmmmm......
Besides all that, it's a good film and you should all go and get it now......I SAID NOW!!!
lox