The peculiarities of language in Québec.

Language in the province of Québec is a bit weird.

As expected, when multiple languages are shared in an area, terms form one languages are borrowed by the other (kind of like how, during France occupation by England, a lot of meats ended up burrowing the French name for them, and still does so to this day). There is plenty of "frenglish" spoken among the French-Canadian population, especially if an English term is much faster and easier to pronounce or write than the French equivalent (such as "gun" instead of "fusil" or "plug" instead of "prise électrique"), but this is not a 100% guaranteed rule, and the french version of the word is sometimes still used, especially if it's part of an expression, such as "être en beau fusil" (being very angry).
Also, there is a similar phenomenon, in reverse, which has been observed with Québec's English population. For example, English-speaking Canadians in Québec go to the "dépanneur" instead of the convenience store. They take the "metro" instead of the subway. They drive on the "autoroute" instead of the highway. And so on.

As for the "Qébécois" language, where to start...

First, there is something called "joual" which is basically French-Canadian slang or patois. Often viewed as somewhat "outdated", many joual expressions are still widely in use while many others, such as "aller faire un tour de machine" (going on a car ride) or "c't'homme là c't'un étrange" (this man is a stranger) are painfully outdated...
In other instances, someone speaking joual could almost sound like they're speaking a completely different language from the point of view of a French person from another country. A good way to completely befuddle a French tourist would be saying something like "M'à aller maller ma lett'" ("I'm going to go mail my letter").

Sometimes, certain expressions used in popular French-Canadian shows enter the lexicon. Some good example would be "Est éffreyante!", a pseudo-joaul way of saying a joke is really good, popularized by the comedian duo of Ding et Dong, or "bouts d'ciarge!", an expression of exasperation used by a character in the show "Le Temps d'une Paix" (granted, both of these specific expressions will be mostly used by older Gen-Xers and older).

Swearing

Oh boy, this can of worm.

French-Canadian swear words tend to be joual versions of ecclesiastical terms. Some of the most popular include:
Criss -> Christ.
Câlisse -> Chalice.
Ostie -> Holy wafer.
Sacrament -> Sacrement.
and the ever popular Tabarnak -> Tabernacle.
There are a few other "lesser" swear words such as:
Maudit -> Damned.
Bâtard -> Bastard (probably as an allusion that Joseph wasn't Jesus' real father...).
Viarge -> Virgin (Mary?).

Just like how some English speaker might self-censor themselves by saying "fudge" instead of fuck or "heck" instead of hell, there exist some "PC" version of French-Canadian swear words, such as "câline" for câlisse", "maudine" for maudit, or "tabarnouche" or "tabarouette" for tabarnak.

One peculiarity of swearing in Québec is that swear words can be "strung together" into chapelet (rosary) to denote strong degrees of anger, displeasure, or unsettlement. A good example would be "Ostie d’câlisse de crisse de tabarnak!".

Swear words also tend to have a a certain degree of versatility. They can be used as verbs, such as "crisser son camp" (getting the fuck out of here). They can also be used as names, such as "le gros tabarnak" (that fat fuck). They can be used as an adjective, such as "est belle en ostie!" (she’s really fucking pretty). They can be made their own special words, such as "décrisser" or "décâlisser" (fucking something up).

Now it's time to talk about the elephant in the room... L'Office de la Langue Française.

If you're outside Québec, especially in other provinces of Canada, you might have heard horror stories which pretty much stipulates that L'Office de la Langue Française is basically some sort of Nazi guestapo, relentlessly tracking down English-speaking people in Québec, specifically to make their life a living hell... Those stories are greatly exaggerated, of course, but every exaggeration has a grain of truth in them.

All right, let's take the infamous bill 101 as an example. It states that no business signs can be in English-only, it has to be bilingual in both French and English (though, no such limitation seems to apply to French-only business signs). Okay, starts a bit off, but let's continue... The bill then states that the French part of the sign must come before the English part. Okay, a bit odd, but not so bad so far, I mean Québec is the only majorly French-speaking province in the country, so that can be understandable... Finally, the bill state that the font used for the French part of the sign must be at least twice as big as the English font. Okay, this is starting to get out of hand...
As you can see, the Office can be quite strict at time and come off as very unfair to English business owners.
Now, I'm not going to defend the Office as I can see that it exaggerates a lot at times (and this thread was not meant to be a political discussion in and of itself), but Canada's history shows that French-Canadian had to fight, sometimes quite literally, to preserve their language and culture. Such struggles taints the worldview of a culture. Even to this day, there are many french-Canadians who still strongly believe that the French-Canadian language and culture is aggressively under attack from the rest of Canada and that the end goal of Canada is the complete erasure of French-Canadian language and culture... All it takes if for one such individual to be part of the Office, and you can see why such laws are made...

On a lighter note, here's pretty much what many French-Canadian sounds when speaking English... :P
My French-Canadian accent!
French Canadian accent
Accent Tag (Québec)
French Canadian Accent Tag

Also, some things Québeckers say...
8 things Québécois people say.

It occurs to me that there is something I forgot to cover here. And while not exactly something about language per say, it does deserve being covered and I can't think of where else I should put this.

Now, many people who are younger than I am in Québec often have two last names. Something I forgot to implement in my games and should probably start doing from now on. Now why are so many people in Québec stuck with two last names? Well, back in 1986, the feminists of the province managed to pass a law which made it illegal for women to take on the last name of their husband. Their reasoning? Women are pressured and coerced into changing their last name when they marry a man. So this law was punt in place, but couples who had been married prior to this point were grandfathered in, but new couples now had to abide by this law.

So when those couples got children, many of them started giving their child the last name of both parents. Oh, but it does not stop there! See, those children grew up and found someone, who sometimes also had two last names, and got together and got children of their own. At some point, I forgot which year exactly, the government had to intervene and pass a law stating that a child could not have more than two last names. Yes, that right, some couple were trying to give their children three or four last names... That's Québec for ya!

Speaking of typically Québec things... Meanwhile à Saint-Léonard...

Oh this made my day :) :)

On the subject of the tense relationships between French and Anglo-Canada, I recently found this article.

It is entirely in French though.