This particular war being over who would come out as the Biggest Colonial Power. Of course, it wasn't enough that the British and French fight one another - they convinced a number of North American Indigenous nations to join the conflict as well, hence the name 'French and Indian War'.
The war started in the colonies but it spread to Europe where it was known as the "Seven Years War". Before you point it out, yes, I know the dates add up to more than 7 years. The conflict started in 1754, but war wasn't officially declared until 1756. But well done for spotting it, you mathlete. I bet you were popular at school.
George Washington has the honour of starting the actual fighting - under orders, of course. He was sent to create a fort in disputed territory. While he was doing that, he crossed paths with a French patrol. Washington attacked, the French retaliated. The British followed up by sending two full regiments of Regulars to the fight. And so it began.
The British fought a losing battle until about 1758 when they got a new Prime Minister, who decided funding the war effort was a priority. Possibly because of the whole French thing. Maybe he ate a bad baguette once. With the added support, the British - along with their Indigenous allies and the colonial militia - began to gain ground slowly but surely. Eventually, the French were driven out of almost all of their territory north of the Caribbean, something we in Britain celebrate with a special holdiday, called "Every day, all year".
So the British won - but they were left with huge war debts. They tried to pay these off with taxes levied from the Colonists they'd defended from the French, who would have had them all eating onions and saying 'Oui sir, non sir' before you knew it. The Colonists objected - leading up to a series of protests, which were part of the unrest that led to the American Revolution. Talk about gratitude. Zut alors!