Black Hawk Down, the closing scene where they all sing the Minstrel Boy.
The Sharpe series of TV films use lots of folk songs, especially Over the Hills (Words tailored to fit the Peninsular War). John Tams played one of the main characters, so no surprises. In Rifles, Daragh O'Malley plays the Salamanca on a tin whistle, pretty sure the tune is later, but it's lovely.
Song Catcher was a lousy film, but great songs.
Didn't the McGann brothers film, the one in 1840s(?) Ireland, have some songs in it?
In the Name of the Father has Lizzy's Whiskey in the Jar.