France

While France didn't jump out of the Age of Discovery "gates" as quickly or powerfully as Portugal or Spain, the French did eventually achieve quite a bit of success in North America. With Central and South America already claimed and controlled by the Spanish and Portuguese, that part of the New World was not in play. The long-hated British Empire had staked their claim on eastern North America. This left the northern part of the continent unclaimed by a European power, and that's exactly where the French headed.

Not only did the French claim much of modern day Canada, but Canadian explorers made their way into the interior of North America by sailing the many rivers and tributaries of the Great Plains. They established mostly positive trading relationships with Native Americans in the Midwest and eventually claim this land for France. This later leads to the French fighting the British in what's known as the "French and Indian War".