I suppose a better way of asking this is why, despite being conquered by the British, that Quebec and Montreal still remain very close to their French roots?
I would have imagined that the British would have tried to at least change the culture or something along the lines to prevent revolt or any harboring animosity against the British?
Trying to forcibly change their culture and end the speaking of French would probably have caused a revolt. The history of empire building is accepting different groups as they are, not as you would force them to be.
It is important to note that assimilation of French language and culture was the ultimate policy goal of the British in Quebec from roughly 1759 until 1867. Governor James Murray headed a military government of the colony in the years after conquest in 1759. The Catholic Church, given its fundamentally anti-revolutionary nature, was willing to assist the British in the pacification of the population, and thus the clergy kept their social position.
As indicated by /u/rick7475, the Quebec Act (1774) would later guarantee the civil liberties of French-Canadians. Quebec as a province, but in particular the fortress at Quebec City, was integral to the defence of British North America. The British recognized it as soon as they incorporated the colony into their Empire, and ensured the cooperation of the local population.
After the Loyalist migration in the wake of the Revolutionary War, the hope was that the influx of English and Protestant settlers would change the demographics of Quebec. However, settlement was confined almost entirely to modern Ontario (from 1791-1867 known as Upper Canada) and the Maritimes. Quebec remained culturally and linguistically distinct.
After rebellions in 1837 and 1838, the Act of Union (1840) incorporated Upper and Lower Canada into a single province. Again, the melting pot that the British desired never came to pass. Montreal was the largest city in Canada during these years, and Anglophones and Francophones lived in harmony. The Anglo-Protestant elite dominated business and politics, but the French Catholic remained the majority population. Meanwhile, rural Quebec remained staunchly Catholic and relied on agriculture rather than commerce.
With Confederation in 1867, the British washed their hands of the issue. The British North America Act (1867) constitutionally enshrined French as Canada's second official language, and allowed for French Catholic schooling and other civil rights.
TL;DR: The British tried to assimilate Quebec, failed, and eventually gave up.
Sources: J.M. Bumstead. The Peoples of Canada
Why would you think that? The population were required to swear an oath of allegiance to the Crown, as long as the French population swore the oath the British government of Canada wouldn't have been interested in their subjects culture. Those French settlers who refused the oath left Canada (Acadia) and went back to France, or to Louisiana.