How did Great Britian's war with France affect the American colonies?

There were both the good and bad effects.

Firstly the colonists were drawn into a war. Whether they wanted to or not did not matter as a part of British Empire they had to fight. On the other side they benefited as the war opened the western frontier for colonization. Unfortunately, the war costed the British a lot and in order to return the money they spent, they put heavy taxes on the colonists and on top of that they put laws limiting colonization of the west.