One of the main reasons European countries explored and settled the Southeast was for economic competition. The larger the empire, the more political and economic dominance! 

As you learned in 7th grade social studies, Marco Polo brought riches and spices to India. Many others wanted to get those riches and spices, but due to the Muslims the silk road was blocked. 

Other countries were in the fight for dominance. Spain was a major contentor. Queen Isabella and King Ferdinand hired Christopher Columbus to find a way to India. Columbus felt as if he could just set sail and go east and he would run into India. Nope, instead he found a whole new world, what we now know as North America. 

England was also a major contentor in the fight for dominance. John Cabot was the major explorer for England. They ended up settling in what we now know as the east coast of the United States (from about South Carolina to Massachusetts and Maine). They were mainly interested in the natural resources, fishing, and forest. 

The other contentor was France. France sent over Samuel de Champlain and Sieur de La Salle. They settled in Canada and the the Mississippi River region (Louisiana). The main interest was fur trade, specifically beaver fur.