Celtic folk music as we have it today (if you mean Irish, Scots, Welsh and other sorts of folk music) almost all comes from long after the time of St. Patrick and events prior to the Council of Whitby and other events. From what I have read "Brian Boru's March" is one of the oldest tunes that still exists in Irish music and he died at the Battle of Clontarf in 1014.
The Chieftains and Brian Boru's March on the Uillan Pipes and Bodhran (small pipes and large hand held drum) and then the rest of the group joining in.http://www.youtube.com/watch?v=9h2Qmx2zp4E
Thanks. I'm guessing that eventually everyone in the isles went to whatever the English church was using (Gregorian?). I wonder what they sang in before. Since St. Patrick and other missionaries were Roman, maybe they used Old Roman chant?