I was always taught that it should, but the Wikipedia article doesn't use the accent at all. I'm British — is it an American thing to ignore the accent? I am preparing some content for an American music site and I'd like to be accurate for as much of the world as possible.
The New Oxford American Dictionary says:
bar•ré |bäˈrā| noun Music
a method of playing a chord on the guitar or similar instrument with a finger laid across the strings at a particular fret, raising their pitch.
ORIGIN late 19th cent.: French, literally ‘barred,’ past participle of barrer.
I never realized that the "é" is supposed to have an accent and is supposed to be stressed. I've always pronounced it like the English "bar", which I now realize was not the original pronunciation.