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.
On top of that, for the reasons above as well as others (including their accent), people from France really dislike listening to people from Montreal speak 'French', and will avoid it whenever possible. This is similar to the way Francophones from Montreal will speak English rather than French to an Acadian, because their accent is really just that bad.
For what it's worth, here is wikipedia's article on Quebec French [citation needed]
http://en.wikipedia.org/wiki/Quebec_French#Mutual_intelligib...
http://en.wikipedia.org/wiki/Quebec_French#Overview_of_the_r...
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").
Put another way: I've never met someone from France who didn't speak ill of Quebecois French when asked, and I've never met an Acadian who felt entirely welcomed in Montreal. They could be exceptions.
http://www.republiquelibre.org/cousture/FRANC2.HTM
Sure, maybe two farmers from rural areas of each country won't understand each other, or a second language speaker who speaks in one accent won't understand the other, but otherwise it's simply pretentiousness.