According to Foclóir Scoile, it should be "bagún". The "a" is a short a sound and the "u" is a long u sound. Short vowels do not get an accent mark while long vowels receive an accent mark.
Because the accent mark indicates a long vowel sound, double accents in Irish words shouldn't raise a warning flag. A couple of examples near the entry for "bagún" are "bácús" (bakery) and "báicéir" (baker).
So did this come from English, did English pass this on, did the two develop this together, what gives? It is also one of few words I find similar between Welsh and Irish.
Well, modern English bacon, Irish bagún (earlier: bacún ), and Welsh bacwn are all descendants of Anglo-Norman bacoun, from Old French bacon -- ultimately a loan-word from Germanic and signifying, of course, "meat from the back and sides of a pig”.
There were Norman lords in Ireland and Wales, as well as in England, so that it's quite natural that Irish- and Welsh-speakers borrowed a fair number of terms from (Norman) French, without any need for these words to have been "filtered" by Saxons.