You didn't attach the map, but I can tell you that what the USA purchased from France in 1803 is known as the <u>Louisiana Purchase</u>. I've attached a map which shows that territory.
Here's some additional information/context:
The Louisiana Purchase doubled the size of United States territory and guaranteed US control of the Mississippi River. President Thomas Jefferson and those favoring the Louisiana Purchase justified it as an act done for the good of the country.
Initially, President Jefferson had commissioned James Monroe and Robert Livingston to negotiate a deal with France to acquire New Orleans or all or part of Florida, as a means of avoiding the potential of an armed conflict in such areas. What they found out was that Napoleon was already set to sell a much wider range of territory to the United States, to finance his European wars.
But then there was a constitutional crisis back home. Did the President have the authority under the constitution to make such a major addition to the nation's territory and spend the nation's funds to do so? Jefferson himself considered pursuing a constitutional amendment, but his Cabinet members disagreed and the measure was sent to Congress for approval. In a statement he made at the time, Jefferson justified the purchase with this analogy: "“It is the case of a guardian, investing the money of his ward in purchasing an important adjacent territory; and saying to him when of age, I did this for your good."
