More taken than given. During the seven years war France and Britain found themselves on opposite sides, along with the Prussians allied with Britain and Austrians allied with France. French Canada which at the time included some other territory beyond modern Quebec in places like Prince Edward Island and parts of New Brunswick today. During the conflict the Royal Navy gained the advantage at see allowing Britain to cut French forces in the region off from supplies and reinforcements from France while Britain was free to deploy its own troops into the region.
For the first few years of the conflict the French still did well thanks in large part with their alliances with a number of powerful first nation polities. However this success was mostly confined to warding off the initial British attempts to invade French Canada, raids and attacking frontier forts. But by 1758 though Britain was bringing in more troops and negotiated a treaty with many of the most powerful first nation groups. Mostly this involved some that where previously neutral throwing their lot in with Britain in return for guarantees and some of the French's allies moved to be neutral. This native allies where extremely important in this kind of terrain where their intelligence and ability to augment the light infantry and scouting abilities of the European armies could be very useful.
British forces in the region then spent the next two years taking the network of forts the composed the main block of the French defences in the region which was relatively sparsely populated with its main purpose being connected to the fur trade and the like. Eventually they worked their way into the core of the French territory by 1759 and French forces in the region's largest settlements where beaten outside of Quebec city and and the city capitulated shortly after this defeat. While in the spring of the next year French forces attempted to retake the city when this attempt was ground to a halt French forces had more or less run out of options and British forces renewed their attack into Montreal taking the French forts there and forcing treaties onto France's first nation allies. At the end of the conflict France was forced to officially recognise the surrender of its conflicts over to Britain.
You may also find more answers your questions in this thread by u/enygma9753.
The war in North America was over by 1760 with the capitulation of the remaining French forces at Montreal, but the Seven Years War still raged on elsewhere in the world. France had hoped to capture British possessions overseas to improve its hand at the peace negotiations, but its European military commitments and its loss to the British navy at Quiberon Bay in 1759 meant they would have difficulty in reinforcing their overseas colonies.
Britain had captured virtually all of France's sugar colonies in the Caribbean by 1763, which were more profitable than the colony in Canada with its less profitable fur trade. During the peace negotiations, France had the option of surrendering Guadaloupe and its valuable sugar trade and retaining Quebec, or getting Guadaloupe back and giving up Quebec to Britain. France chose Guadaloupe sugar over Canadian furs, while Britain suddenly became new masters of some 70-80,000 French Catholic subjects -- who resented Britain's conquest of New France, but also felt abandoned (and even betrayed) by France's willingness to cede New France and leave them to an uncertain fate.
How Britain dealt with Quebec and its generous accommodation of French Canadians and their native allies would help set the stage for rebellion in the Thirteen Colonies within 15 years.