Early European possessions in North America included Spanish Florida, Spanish New Mexico, the English colonies of Virginia (with its North Atlantic off-shoot, Bermuda) and New England, the French colonies of Acadia and Canada, the Swedish colony of New Sweden, and the Dutch New Netherland.
England
Polo never came to North America and was only in China. He did not claim land.
Spain
French explorers first claimed lands in present-day Canada, particularly along the St. Lawrence River in the early 16th century.
Spain was the first country to claim land in North America.
The Kingdom of Spain was the first country to claim lands in North America following the successful expeditions of explorer Christopher Columbus. The first European city founded in the New World was Santo Domingo in 1497 which was founded in the present day Dominican Republic. The first city that was founded on the continents of North or South America was the city of Cumaná in modern day Venezuela in 1501.
Portugal was the only country that did not claim land in North America.
He was a Viking explorer, and was the first European to set foot in North America.
Various Native American tribes inhabited North America, but they did not claim possession of the land, since they believed it belongs to everybody. So, the colonists were really the first people to "claim" the land.
North and South America
Samuel de Champlain claimed the land that is now known as Quebec, Canada, in North America. He established the French settlement in Quebec City in 1608, which became the capital of New France.
France is generally considered to be the first European country to explore, then to stake a formal claim to, the lands along the St. Lawrence River in North America. As early as 1534, a French explorer by the name of Jacques Cartier was sent across the Atlantic Ocean by the French king (Francis I) with the explicit purpose of establishing a French presence in the New World.