Visiting Montreal was on the top of my bucket list, so I was dying to visit! I was finally able to make it by planning to come here after my cousin's wedding in Vancouver. I really liked the city and how many parks there were!
You can get around with only knowing English, but I highly recommend at least picking up some rudimentary French. Everyone will know English, but some French will get you far. Getting around the city is pretty intuitive.
To get around, I also recommend getting Montreal's version of a transportation card called a OPUS card. You can get one at the airport by just following the signs that say "747 bus". The 747 is an express bus that goes right from the airport to downtown. It typically costs $10 CAD. So when you're getting your card, I recommend selecting one of the 1/3/7 day passes that are also offered. Chances are you'll use it and it covers this particular bus, along with all metro and bus rides. Getting the typical one-way fare will NOT be enough to cover the cost of the 747 bus. Also, if you are getting a weekly pass, it only covers Mon-Sun (I think). For example, if you get it on Thursday, then you're essentially losing Monday-Wednesday.
For each section, bolded places are the one I recommend. To make an itinerary out of this, you can pick one thing from each section to structure a “day”.
For these attractions, I mostly only passed through these neighborhoods.