Why did President Jefferson want to buy the city of New Orleans from France?
New Orleans controlled the mouth of the Mississippi River which was essential to trade and the development of the Northwest territory.
As the Northwest territory was settled and developed the Mississippi River was essential to trade. The Appalachian mountains were a barrier to trade between the Northwest and the Atlantic coast. The crops from the Northwest were floated down the Mississippi River.
Spain had allowed the Americans to freely ship down the Mississippi and trade. Jefferson feared that the French wanted to establish an America empire that would restrict access from the northwest to the rest of the United States.
At first Jefferson only wanted to purchase the city of New Orleans to ensure American access to the Mississippi River and trade routes to the eastern America. The French offered to sale the entire Lousiana Territory instead of just the city of New Orleans.
This purchase enabled the vast expansion of the United States.