It depends on your budget, actually. If you have the dough, The plateau Mont-Royal is very french and awesome to live in; shops, cafes, very european. If you're not very rich, go to the east, maybe around marché maisoneuve, or in St-Henri: cheaper, a bit dirtier, but still not that far from downtown by metro (subway). There's also all the area around Universite de Montreal around Queen Mary, but you're farther away from everything. If you like the suburbs life, go to Longueuil or Varennes; they're on the South shore of montreal and agian, not too far from the city by bus or metro. Lastly, if you don't necessarily want to live in a completely French area, look around Jean-Talon metro; still alot of frnech but it's right beside little Italy and there's a huge market for groceries where you'll bump in dozens of different ethnicities in every store.
Lived there for 23 yrs.,