Aside from ousting the French from a substantial part of what was to become the United States, as well as removing the French from Canada, thereby giving the British unrestricted access to million of acres of contiguous territory, the French and Indian War all but spelled the end Native American influence in the eastern colonies.
Because many of the American Indian tribes supported the French, particularly in the Midwest and Upper Midwest, when the French were defeated and stopped their material support of the Indians, those tribes were forced to turn to the English for support who, in many cases, forced treaties on the Indians that effectively denied them access to lands they had lived on for hundreds of years. The treaties also opened thousands of square miles to westward expansion, which also helped to displace Native Americans and hastened the end of their freedom.
In addition, American colonial troops fighting alongside the British during the war were generally treated as untrustworthy amateurs, treatment that bred a deep-seated and lasting dislike of the British military. American troops also saw gross mis-management of the war on the part of the British, including the defeat of large British armies by the French and Indians, and this confirmed the belief among American colonial troops and, most important, American officers that the British could be beaten. The Americans took this knowledge and experience with them and put it to use during the Revolution.