...who would never have sold it to the British, as he then turned around and used the money to wage war on Britain.

But technically, Louisiana was still under Spanish rule at the time of the sale, as it had been traded by Spain to France for the possession of a kingdom in Italy (taken as part of Napoleon's Italian campaign), but never officially occupied by the French. Napoleon's big plan involved reviving the sugar trade from the Caribbean, after retaking the island of Santo Domingo from the slave army of Toussaint L'Overture, and using the Louisiana Territory as a market for the sugar. Unfortunately for the French army in the Caribbean, Toussaint's army, combined with yellow fever, proved more than a match for them. Without Santo Domingo, the plans for the sugar trade were worthless. Napoleon decided to cut his losses by offering to sell the whole territory for $15 million instead of merely the port of New Orleans for $10 million, as Jefferson had suggested.

The territory was officially turned over by Spain to France the day before it was turned over by France to the US. The French revolutionary tricolor only ever flew over the city of New Orleans and the fort at St. Louis, for one day each, after which it was taken down and the Stars and Stripes was run up the flagpole in its place.