Pictures do not prepare the visitor for the awe inspiring sight of the Basilica's interior. The word awesome is used far too casually these days but here is a case where its use is entirely called for: Notre Dame is truly awesome.
I was taken aback by the altar's spires, effectively presenting a church within a church! (When illuminated at night as part of the "Let there be light" show, for a second I thought it was a spaceship! Ancient astronaut theory aside...)
Tours are available for a fee and one tip I suggest is to take the walking tour of Old Montreal. The tour will take you here and additional sites. You'll then be given a ticket stub that gets you back into the Basilica for free that day.
The 8:30pm showing of "Let there be light" offers a recollection of events that does not claim to be 'historically accurate'. (There's a disclaimer of sorts before the show). You'll be given a headset that can tune into spanish, french, chinese or english versions of the presentation. The show is hosted by the basilica's architect, or rather the ghost of, and you'll see dramatizations of key moments in Montreal history.
The production values and over the top dramatization are unintentionally quite funny-- who knew Marguerite Bourgeoys wore makeup?
All kidding aside, the best part of the show is when the various parts of the basilica are revealed. Afterward, you'll have about 10-15 minutes to take photos.
Even as a formerly religious person turned heretic, I found the structure impressive. For the faithful it must be an even more moving experience. For the tourist, it's a must-see.