Montreal native here, though I don't live there now.
Also very interesting, though expensive, are the Biodome and the Insectarium. The Biodome was originally the Velodrome for the 1976 Olympics, so you can also tour the Olympic Stadium while you're there. These are near the Botanical Gardens.
If you go to one of the markets early in your stay, you can pick up local produce, gourmet cheese, charcuterie, etc. to eat for the next several days. There are also mini-farmer's markets on some street corners, mostly for produce rather than the gourmet foods. I second getting poutine and bagels and would add: croissants from the Duc de Lorraine bakery (on Cote des Neiges Rd near Queen Mary Rd). That is near St Joseph's Oratory, which is arguably of greater historical/religious significance than the Basilica, although definitely not as beautiful. Also, the cathedral (Marie Reine du Monde) is a scale replica of St Peter's in Rome.
Fun for kids is the Parc La Fontaine, in the Plateau Mont-Royal neighbourhood (full of arty boutiques and eateries). The parc has a puppet theatre, you can watch people play petanque (French bocce), there are walking/biking trails, a pond, and playgrounds.
In the touristy areas and stores, most people will be bilingual, but if you go to the east end, you are more likely to be surrounded by monolingual francophones. One of my teachers grew up in that part of town and didn't meet an English speaker till he went to university. If you don't speak French, you might find this interesting and exciting, or frustrating and inefficient.
Oh, and Stash's is where the rehearsal dinner for my wedding was held--my MIL is Polish.