Been there 4 times; the best time to go kiting is around labour day weekend (1st of september); I think that september is usually when they have the strongest wind.
This year we are trying it in august to get some warmer weather (my GF doesn't kite)
Last time I was there we had +30 knots all week long. The nice part is that you have access to flat water spots (chiasson office, pointe campbell); waves (miscou island); nice chop (pointe canot) etc... you can kite in la Baie des Chaleurs. This is where the St-Lawrence river meet the Antlantic Ocean. You can also kite on the Ocean side where the water is a lot cooler though.
It doen't matter on which side that the wind is coming since there are so many kiting spots. You have also lots of really nice beaches.
this is a link to Adrien's houses to rent (used to be Eric Girard's houses); that gives you access to an amazing nice flat water private spot.
We go back every year; people are really nice; the seafoods are fresh and very cheap. The beaches are also really nice and aren't overcrowded. If you like kiting and the outdoor you have to go there at least once in your life.