As Frédérick says, the competition these days is always held from the middle of June until the end of July, give or take a few days. In June, there is one display a week, and in July, there are two a week after the first week.
In terms of other activities in Montreal, the Jazz festival (
www.montrealjazzfest.com) is usually the last week of June and the first week of July. The interational comedy festival (
www.hahaha.com) just started this week and runs until the third week of July.
There's also the first nation's powwow at kanawake (
www.kahnawake.com)
in mid-July, the Francofolies (
www.francofolies.com) French music festival in early July; African music also in July (
www.festnuitafric.com).
A good place to find more information is the Montreal tourism site at
www.tourisme-montreal.org
If you come in July, you can chose what other activity to do and, if you come for 8 days, see three displays!
Cheers,
Paul.