Final answer:
William Pitt was the British Prime Minister who aimed to conquer French Canada during the French and Indian War. He raised a large force and cut off French supplies through blockades, which contributed significantly to the French defeat in North America.
Step-by-step explanation:
The British Prime Minister who set the goal of conquering French Canada during the French and Indian War was William Pitt. Pitt, recognizing the strategic importance of North America, mobilized an impressive force of 45,000 troops, comprising British regulars and colonial militiamen, to engage the French. His commitment was evident as he subsidized the colonies for their wartime participation and employed the British navy to blockade ports, preventing French reinforcements and disrupting French trade. This strategy notably affected the French forces and their alliances with Native Americans. In 1758, thanks to financial support and military vigor, the British captured Quebec and, subsequently, Montreal in 1760, eventually leading to the collapse of the French empire in North America. William Pitt's foresight and resources were paramount in turning the war in favor of Britain and achieving victory in the Seven Years' War.