Final answer:
France and Britain were the two nations that fought for control of North America in the early 1700s, with Britain eventually prevailing in the conflict known as the French and Indian War.
Step-by-step explanation:
The two countries that fought for control of North America in the early 1700s were France and Britain. This struggle for dominance is known specifically as the French and Indian War, which was part of a larger series of conflicts known as the Seven Years' War when it extended to Europe and other regions. During this time, both nations engaged in war and formed shifting alliances with various native peoples, who played crucial roles in the outcomes of these wars. Ultimately, with the 1763 Treaty of Paris, Britain emerged victorious, gaining control of New France and thus dominating the majority of eastern North America.