The French and Indian War connects to the Atlantic world in two important ways. First, it removed France from playing a major role in the Americas. Second, it eventually helped to create a new country that would come to be very important in the Atlantic world.
Before the French and Indian War, the French had a potentially strong position in the New World. They held what is now Canada and they had a claim to what later became the Louisiana Purchase. These territories made France an important player on both sides of the Atlantic. With France’s loss in the war, it lost most of its base of power in the Americas and became a less important player in the Atlantic world.
The French and Indian War also led fairly directly to the American Revolution. The American Revolution, of course, created the United States. This meant that there was, before 1800, a new country that would dominate the western part of the Atlantic world. The US was not yet dominant in 1800, but its presence was beginning to change the Atlantic world.