At LEAST three alternatives:
1) KOA south, not the closest campground but quite a nice place. They have a shuttle bus to and from downtown Montréal during the summer time.
2) Camping Alouette also on the south side of the river. They also have a shuttle service to downtown Montréal.
3) Marina Port de Plaisance. The closest campground to Montréal right on the St Laurent river.Their shuttle is a boat leaving your campsite for a 15-20 minute cruise to downtown Montreal.
Those 3 campgrounds are easily accessible with your class C.