There were many countries that did not have a claim to lands in North America. It would probably be more prudent to discuss the European countries that actually had claims.  England had claims along the eastern seaboard of present-day United States and after the French and Indian War, much of eastern Canada. The Spanish had claims in Mexico, the southwest United States and Florida.  The French were in Canada, particularly in the area around Quebec while the Netherlands at one point were around the Hudson Bay.  A country that had claims in the New World but their territories were in South America.  The Treaty of Tordesillas was an agreement between Spain and Portugal that kept the Portuguese out of North America.