Spain was trying to conquer the land along the West Coast and the Southwest, and Florida, although most of that land was still ruled independently by the Californians, the Navajo, the Pueblo, the Apache, the Ute, the Paiute, and other native people. Spain, Britain and the United States were arguing over who should control the Pacific Northwest, but most of it was really still ruled by the Chinook, the Nez Perce, the Shoshone, and other native people.
France wanted to control the middle of North America: the Mississippi Valley and the Great Plains, though again most of that land was still ruled by the Sioux, the Cree, the Shawnee and the Creek. In fact, the Shawnee, under Tecumseh, were fighting a big war for their land.
In the East, the newly created United States of America really did control most of the East Coast except for Florida, and also most of the Midwest, although there were still areas really controlled by the Cree, the Shawnee, the Cherokee, and the Algonquin.
But France was involved in a big war with Britain, Russia, Austria, and Sweden, and needed money to pay their army. In 1803, Napoleon, the emperor of France, decided to sell France's part of North America to the United States for $15 million dollars (which would be a lot more in today's dollars, but it was still a total bargain). Thomas Jefferson, the President of the United States, agreed to buy the land. The Louisiana Purchase made the United States twice as big as it had been before, at least on paper - but the Native Americans still really controlled most of the land.