In the Ohio River Valley both France and Britain thought they owned it. The argument turned into a war and it lasted 10 years. Britain and the colonists fought against the French and the Indians (because they were friendly to them.) That is why they called it the French and Indian War.
At first, the British were losing because of they bright red jackets so they were easily spotted. Then it changed when in 1759 when the British was in power of Quebec the capital of Canada. So the French lost all of Canada they owned.
In 1762 they asked for peace. In 1763, a peace treaty gave the right to control Canada. The British also won the land between the Mississippi River and the Appalachian Mountains. It gave the British land but debts as well it cost 30 billion dollars today. Extra information after the war the British created the Proclamation of 1763 because the natives fought for the way of life and settlers also got killed so that's why it was made.