Earlier quoted context omitted.
I think you're exaggerating. Parisians may tease Quebecers, but that's just to keep themselves in teasing shape. Teasing is a sport, you gotta practice. Most French people will be able to understand most Montrealers. It should be noted that France itself has many regional accents that are quite strong. Also to be noted, there is a steady flow of young French people immigrating to Montreal.
Most French people will be able to understand most Montrealers sometimes, in the same way that someone from Britain would be able to understand a Cajun sometimes. The language is very divergent, with franglais words sprinkled here or there, shortened words, differing word usage, etc. On top of that, for the reasons above as well as others (including their accent), people from France really dislike listening to people…
I'm a francophone, born in Quebec. I have never seen a francophone (from anywhere in the world) speak in English to another because the accent was too strong. Most francophones in Montreal actually speak pretty bad English, at least once you leave the technical spheres, and any Quebecois can speak something closer to "international French" when he knows an European is listening.
A large portion of my classmates at university were French people. They had no trouble understanding the local accent. They might be puzzled by some special expressions we have for snow, for "take a chair", for shortened forms ("je ne le sais pas"->"jelsépa"), swear words, etc. but nothing that can't be explained fairly quickly. The difference between French from France and from Quebec is important but I'd say comparing it to Cajun is exaggeration. It is not my impression that French people dislike Montreal French, but rather that they find it amusing at first (it sounds like a rural accent) and eventually just get used to it. Many Quebecois humorists and singers are popular in France as well.
Franglais is a large debate, but in short, the French are as guilty of it, if not more than the Quebecois. Many words like "email" or "shopping" tend to be said in English in France but in French in Quebec ("courriel", "magasinage").