The French accent is a good clue. Of couse some Irish settlers to Quebec became integrated with the French speaking population and so were French speaking despite having English/Irish names. I think most of the Irish are in Montreal. If you do any research in Quebec I'd start there.
The previous post regarding Irvings and New Brunswick is also a good tip. I quickly googled old KC Irving (there is very wealthy family of Irvings from New Brunswick, KC was the founder of the business). KC was from Bouctouche, New Brunswick. Bouctouche is in the French (Acadian) part of New Brunswick. You could start in Bouctouche and work out from there.
J.