The Louisiana Purchase is seen as such a great deal for the United States but what's stopping the Americans from just taking the territory without paying anything to France? Napolean sold Louisiana Territory for cheap because they couldn't defend it properly due to the loss of Haiti.
Were Franco-American relations too strong for Jefferson to contemplate invasion? Were Jefferson afraid of France's response? Were the American military too inferior to French colonial troops in Louisiana at the time? Would the invasion cost more than just outright buying the place?
Although a pro-British camp existed in early US politics, the United States in it's early history tended to be very close with France, as the United Kingdom didn't hesitate to threaten the new country's sovereignty at every chance it got, and France had played a decisive role in the fight for independence. This is exemplified by the War of 1812, which is often glossed over in U.S. History textbooks; taken in the context of world history, the war is nothing more the United States' intervention in the Napoleonic wars, where it entered on the side of France (consequentially, yes, this means that the United States lost that war).
Because the countries were so friendly, and needed each other to fight off the British, the United States would never straight-up invade French territory, especially as the new country desperately needed allies.
Thus, the sale was mutually beneficial; France would have probably lost Louisiana to the English had they not sold it, so Napoleon was much happier to see it go to the United States. Plus, Napoleon got a fair bit of cash that he could use to keep trying to conquer europe with. The US, instead, got a whole lot of new territory, and they strengthened their ties with a friendly country.
edit: typos