Hi Phideas1,
Not Irish, but Scottish (and I think that's what Bob Clarke called it in his commentary - "a Scottish lullaby").
I'm pretty sure the tune is "The Flowers of the Forest", a lament written for the pipes over the Battle of Flodden Field in 1513. It's most commonly played at funerals; I'd have to go back and check, but there's a funeral with a piper playing in the film, and I suspect that's what the pipes are playing there as well. Like most pipe tunes (and most Gaelic tunes generally) it's in a modal scale, and the tune at the end of the film varies a little bit from the pipe tune because it's adjusted into the musical scale more common to our "western" ears.
I found a version on Youtube (YouTube - Dick Gaughan - Flooers o' the Forest (
http://www.youtube.com/watch?v=cJIrAkJnS1I)) that kinda de-wails it [;-) !!] and might make the melody more accessible if you're not used to listening to the pipes.