The main historical significance of the French and Indian War is that it helped bring about the American Revolution.
Before the French and Indian War, American colonists were relatively content to be British. The British more or less left them alone to tend to their own affairs. They were also aware that the British were their defense against the French in Canada. For these reasons, they had no desire to be independent. After the war, this changed.
The war expelled the French from North America. In doing so, however, the British incurred massive costs. They wanted the colonies to help to defray those costs. Therefore, they started taxing the colonies and doing more to enforce British law in the colonies. These acts made the colonists unhappy. In addition, with the danger of French invasion removed, there was less need for British protection.
For these reasons, the American colonists started to feel unhappy about British rule after the French and Indian War. Their resistance to British actions brought reprisals from Britain which further strengthened colonial grievances. This cycle led to the coming of the Revolutionary War not much more than 10 years after the end of the French and Indian War.
The French and Indian War completely changed the national dynamics in North America with the British acquiring land and the French being essentially expelled. While this, and the impact of the war on deteriorating relations with the American colonies, is important, I would like focus on a small group that was greatly impacted by this conflict. This group is called the Acadia, a French-speaking culture from around Nova Scotia. They had peacefully co-existed under British rule but with the two countries now at war, the British demanded that the group swear allegiance to England, and even fight against their homeland. The oath also would have forced them to give up their Catholic faith. This was not acceptable to the Acadians and they refused allegiance to the British. The British army saw this as a sign of rebellion and expelled the Acadians from their lands. The Acadians, having been exiled from Nova Scotia, headed on a long journey through the Thirteen Colonies that saw them settle in Louisiana. While their story may not be well known, their culture is. The Acadians became what we know call the Cajuns, a French culture in the United States.