From Britannica:
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French and Indian War

North American phase of a war between France and Britain to control colonial territory (1754–63). The war's more complex European phase was the Seven Years' War. Earlier phases of the quest for overseas mastery were King William's War (1689–97), Queen Anne's War (1702–13), and King George's War (1744–48). The North American dispute was whether the upper Ohio River valley was a part of the British empire or part of the French Empire; the bigger question was which national culture would dominate the heart of North America. British settlers were the majority in the coveted area, but French exploration, trade, and Indian alliances predominated. In 1754 the French ousted a British force, including a colonial militia under Col. George Washington, at Fort Necessity, Pa. Until 1757 the French continued to dominate, but in 1758 Britain increased aid to its troops and won victories at Louisbourg, Fort Frontenac, and Fort Duquesne (Pittsburgh). The final British victory at the Battle of Quebec (1759) led to the fall of New France (1760). In the Treaty of Paris (1763) France ceded its North American territory to Britain.

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More on Washington from Wikipedia:

Washington's goal at the outset of his military career had been to secure a commission as a British officer, which had more prestige than serving in the provincial military. However, the British officers had disdain for the amateurish, non-aristocratic Americans. Washington's commission never came; in 1758, Washington resigned from active military service and spent the next sixteen years as a Virginia planter and politician.