How did the Seven Years' War transform the relations between Europe and the North American colonies?
This question should more properly ask about the relations between England and the North American colonies. After this war, France no longer had any North American colonies. Therefore, the relationship was really just between England and the colonies.
The relationship between England and the colonies was fundamentally changed by the war. It is fair to say that the war was the factor that changed the relationship and led to the American Revolution. This is because the war caused England to need to take closer control over the colonies.
After the war, England’s finances were in poor shape. The war had been expensive and there were debts that needed to be paid. Therefore, the English government did two main things. First, it tightened its enforcement of laws (particularly laws having to do with trade and smuggling) in the American colonies. Second, it imposed taxes on the colonies to help defray the costs of the war. These actions angered the colonists greatly. They had become used to being left alone in the past few decades and did not like having the government exerting control over them in new ways.
Thus, the war severely weakened the relationship between the British government and the colonies.
The Seven Years' War, also called the French and Indian War in North America (1756-1763), was a worldwide conflict. In North American, the conflict involved fighting for control of the Mississippi River basin and Ohio River Valley between the French and British. The British victory meant that the colonies took over this land running throughout the Ohio River Valley and southward, to the east of the Mississippi River.
After the war, the American colonists wanted to move into the land that the British had conquered from the French, but the English throne, wary of causing conflicts with Native Americans in the area (such as Pontiac, chief of the Ottawas), prohibited colonists from entering the territory that was west of the Appalachian Divide. The result was that colonists were angered by this proclamation and the limit on their freedoms. In addition, the English throne, in debt because of the war, re-instituted the Navigation Acts after a long period of what was called salutary neglect. The colonists, long used to non-infereference in their trade and economic affairs, reacted by beginning the process of resistance that would lead to the Revolutionary War.