Please be aware that this is not an attempt to malign the language of Québec in any way.
In a way, one might be able to say that the language of Québec isn't French, from a historical point of view. The country of France is so called because it is the result of of the centralization policies of the kings of France. In the Middle Ages, France referred to the Ile-de-France, the region immediately surrounding Paris. The other parts of what is now France spoke their own dialects, similar to, but different from, the dialect of Paris. The concept of a national "French" language did not yet exist. (The official language of the kingdom of France was Latin until the reign of François I.) For example, the language that was imposed on England in 1066 by William the Conqueror was not Francien (the "French" of the Paris region) but Normand (the "French" of Normandy). This is why the English words we label as borrowed from French are not identical to the French words themselves: carpenter v. charpentier, mercer v. mercier, for example. The dialect of the Parisian basin did not truly become seen as the national language until the Revolution, when the need for such a language was first identified.
Now, most immigrants to New France came from from Normandy, the Maine, and Anjou, in the case of the Québécois, and from Saintonge and Poitou in the case of the Acadians, between the early 17th century and the middle 18th century. Their speech was different from the speech of the Parisian region, which had not yet been defined as "French." The standardization of French in France took place after the Québécois left the Mother Country. Therefore, the modern language we call standard French is descended from one medieval dialect, and the modern language we call Canadian French is descended from another.
Furthermore, the "French" that we are familiar with today is based mainly on the idioms of the aristocracy and the academics. If you read Molière, you'll see that the dialects he uses to represent peasants, particularly those from the provinces, speak very much like French-Canadians.