The inaptly named French and Indian war was fought in North America by the French and their Indian allies against the English and their Indian allies.
This war started when the French and the English fought for land in the Ohio River valley. However, this was a theater of the Seven Year's War, which was being fought in Europe at the time.
The war lasted seven years, from 1756-63. The English won the war; however, the French had more early victories, defeating George Washington and Edward Braddock.
However, the English, led by James Wolfe who fought and died in the Battle of the Plains of Abraham, captured Quebec in 1759. The French tried to retake it, but failed. They soon gave up and in 1763 ceded most of their possessions in North America to the English.