Many of the 'IRA' songs were set to existing tunes.

Also, there are numerous threads on 'Irish' songs which aren't originally Irish.

A few examples, but you can search the forum for others

Danny Boy (Words by an Englishman, tune MAY be originally from Scotland)
Black Velevet Band (originally set in Barking, Essex - now in London)
Wild Rover (collected in Norfolk, but derived from a 17th C song with known author)
Wild Mountain Thyme = Braes o' Balquidder (Scottish)

(and Green Fields of France = No Mans Land, of course)