There were at least three primary impacts of the French and Indian War, two of which are evident and one perhaps not evident and certainly unintentional.
First, the most obvious impact of the war was the ceding of Canada and a substantial portion of what would become the United States to Great Britain. The French had controlled Canada, as well as most of the upper Mid-West of what became the US from early in the 17thC through 1763, and the loss of those territories ended essentially a never-ending source of conflict between Great Britain and the Colonies, on one side, and France, on the other side. With the end of the war, Great Britain acquired thousands of square miles of territory that had effectively been under French domination for more than 100 years.
Second, France, helped along by Great Britain's often dismissive policies toward American Indians, constantly encouraged disaffected American Indian tribes to resist the advance of the "English," and this ultimately hastened the dismantling of American Indian cultures in British North America and later the United States. France's policies were effective, however, in impeding British colonization into the Midwest and, particularly, the Upper Midwest. With the defeat of France, the Indians who had looked to the French for comfort and goods, were forced to turn to the English and, more important, make treaties with the English that allowed unrestricted access to Indian tribal lands. The Indians, of course, didn't realize they were giving the English complete access and ownership of their land because they did not recognize the "legal" concept of land ownership.
Third--perhaps the unintended impact of the war--is that Americans who fought alongside the best army in the world (the Brits) discovered that the British could be beaten. Several substantial British Armies (as well as American colonial troops) were beaten by the French and Indians, and the weaknesses of the British way of fighting was not lost on several American officers who fought alongside them. In addition, because British officers often treated American colonial troops as largely untrustworthy allies, many American troops learned to despise the British Army, not to fear it. Even though there is no way to measure the impact that British military condescension had on American troops, scholars are now discussing the possibility that the start (figuratively) of the American Revolution began in the French and Indian War.