Yep, Grand Prix du Canada this weekend. The actual race is on Sunday but everything will be booked from Wednesday until Monday. It is a fabulous time to be in Montreal BUT people reserve months in advance to get a hotel room and they do pay a premium rate. One other possibility - airbnb.
http://www.airbnb.com/
Airbnb is a reputable short-term house/apartment rental site. Some of the people registered will want to share their lodging but some actually have places to rent.
Good luck. I hope you find someplace to lay your heads.