Yes, they do. First, the accent is really different. Quebec's accent is sometimes so "thick" that a French from France has trouble understanding someone from Québec. However, when I watched TV or movies from Québec, the accent was really light, almost parisian. Then, there is a lot of different vocabulary: what I find funny is that on one hand, Québecois tend to replace english words with french words (in France, we say "weekend", in Québec, they properly say "Fin de semaine"), but on the other hand, they use a lot of english words while in France we have french equivalents (in Québec, they say "un party", while in France, we will say "une fête"). I will not let true Québecois correct me or give other significant examples.

On this link, you can find many exemple. I am not come from Quebec so i cannot tell if there are all really used ! http://www.chezmaya.com/07/expressions.htm The famous one is Quebec people call a car= "un char" instead of "une voiture" for french. They also use many english word in the vocabulary.

As a Québecois I agree with Clément. The accent is really different, also we are often shortening word in spoken french (but we don't write like that). And adding "tu" Tu sais tu = Est-ce tu sais T'sais = Tu sais Y = il (although it's 50/50) y é grand (il est grand) a = elle (50/50) a va la (elle va là) Series and movies are often spoken in "international french" or sometime they even dub it in less Québecois french. We will also speak with a lot more "é" even if the words don't need it (like older France french). Funny example recently. In a Larousse for learning Spanish it was written è should sounds like Mai (the month). But in Quebec it's pronounced more like in english. "Mé" or May. So it made no sense until we found out it was from France. They should have used the word "mais". Although the written french it's pretty similar, except for expressions and some different words to describe things. But as a second language I don't think you will have trouble with a Quebec french teacher as they will use proper grammar and pronunciation. It's mostly native spoken language that is different.