How did jefferson ultimately end up purchasing the entire louisiana territory

The Louisiana Purchase (1803) was a land deal between the United States and France, in which the U.S. acquired approximately 827,000 square miles of land west of the Mississippi River for $15 million.

[T]his little event, of France possessing herself of Louisiana, ... is the embryo of a tornado which will burst on the countries on both shores of the Atlantic and involve in it’s effects their highest destinies.1

1805 Map of Louisiana by Samuel Lewis; courtesy the Library of Congress
1805 Map of Louisiana by Samuel Lewis; courtesy the Library of Congress
President Thomas Jefferson wrote this prediction in an April 1802 letter to Pierre Samuel du Pont amid reports that Spain would retrocede to France the vast territory of Louisiana. As the United States had expanded westward, navigation of the Mississippi River and access to the port of New Orleans had become critical to American commerce, so this transfer of authority was cause for concern. Within a week of his letter to du Pont, Jefferson wrote U.S. Minister to France Robert Livingston: "every eye in the US. is now fixed on this affair of Louisiana. perhaps nothing since the revolutionary war has produced more uneasy sensations through the body of the nation."
- Louisiana Purchase facts

The mountains on the east would be taller