It is a question I ask myself sometimes, especially around Saint-Patrick's Day, which I started celebrating in Montreal. On Montreal's flag and coat of arms, you can find the Irish shamrock, alongside the French fleur de lys, the English red rose, and the Scottish thistle. These people founded and built Montreal, so they are deservedly represented, but the motto of Montreal: "Concordia Salus", "Salvation through harmony", is as hypocritical as it can be. There is nothing, there has never been anything harmonious about Montreal, certainly not among it's various groups. It is a city of division and conflict. The Protestant English and Scots dominating and exploiting the conquered Catholic French, then Irish immigrant coming in, some of them mixing with the French majority (especially since many Irish orphans were adopted by francophone families), some of them not overcoming the language barrier. Montreal is a city of conflicts and division.
So how Irish is it? It's climate is closer to Ireland's than France's. The beers are certainly not as dark, in general, but we sure drink a lot. And there are the names: Johnson, O'Neil, Farrell, McMullen, Murdock, etc. And I am just naming some off the top of my head. Names you find among the francophone population. It is traditionally Catholic, unlike France it did not quite divorce from it and its Catholicism is more akin to what you find/found in Ireland than in, say Italy, more cultural and less devout (I mean generally, and maybe it is wishful thinking). Our attitude towards British monarchy is certainly the same, going from disdain to downright hostility. But unlike an Irish city, Montreal is not in a republic. Which is sad. Maybe I am seeing a relationship that is not here and maybe my love for Ireland makes me exaggerate, but I do think Montreal is maybe more Irish than it is anything else.