A distinction should be drawn between formal French and social French. From the standpoint of formal French, there's no difference; it's an international French that is used in Quebec, in France and elsewhere. However, social French differs from region to region. The strategy that the Saint-Jean Campus has adopted, for example, is to have students learn social French not in courses, because they learn formal French there, but in various places and programs outside the courses, where they can learn social French.
This is often an emotional French. So it involves small emotional words that you'll often hear among anglophone students when they speak French. They say cool man—in English—because it's an emotional French. I think it's important—you're right—that we “teach” that emotional French, not necessarily as part of the formal courses, but, for example, in the residences, the corridors, at informal meetings, tutorials between anglophones and francophones and so on. So French isn't learned just in the classroom, but also in informal venues.