Many Montreal restaurants don't have a license to serve wine, but this is a good thing, because you can bring your own and there's no corkage. Combined with the competitive Montreal restaurant market, it makes for a cheap way to eat and drink very well. Look for restaurants with the sign "Apportez Votre Vin".
Wine can be bought at one of Quebec's SAQ (Societe des Alcools du Quebec) stores or at a depanneur (corner store).
Away from the big streets on the Plateau is good AVV hunting territory. Les Infideles on Rachel (near St Hubert) is a great example, but there are lots of cheaper places too. The closest SAQ is on St Denis just up from Duluth.
Updates
You don't have to buy your wine from the SAQ, though it does have the widest selection. In Quebec you can buy beer and wine from 'deps', or depanneurs, local corner stores whose name means 'the guy who saved me'. They're open late, there's literally one on every corner, and they generally won't ask for ID. 
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