The French and Indian War changed the relationship between the colonies and Great Britain in many ways. One was that the territories gained by the British as a result of the war led to almost immediate conflict, as the Crown tried to avert war with Native Americans by stopping settlement west of the Appalachians. This created tensions between the British ministry and western settlers as well as wealthy land speculators.
Another change in the imperial relationship was a result of the tremendous debt incurred by the British government, as well as the additional expenses of administering (and stationing soldiers in) the vast territories gained as a result of the Treaty of Paris. The British tried to service this debt first by tightening restrictions on trade with the colonies and, at least once, by passing an "internal" tax in the form of the Stamp Act. The Stamp Act was highly controversial, and met with violent protest, because it seemed to violate an age-old protection enjoyed by British subjects--the right against taxation without representation. Additional duties on imported goods did not meet with these theoretical objections, but they did hurt the pocketbooks of colonial merchants and ordinary city-dwellers. Moreover, to many people, they represented a pattern of abuses that constituted an assault on colonial liberties.
There were other ways in which the French and Indian War altered the relationship--British ministers were unimpressed, for example, with the willingness of colonial legislatures to provide funding for their own defense, and colonial militia bristled at the attempts of British officers to impose harsh discipline on them. But the imposition of the Proclamation of 1763, the Stamp Act, and other controversial measures was primarily responsible for driving a wedge between Britain and its colonies in the wake of the French and Indian War.