Maybe the British didn’t know that Jefferson threatened through a diplomat in France to ally with the British (among other things), if the purchase wasn’t completed. The French were also largely considered by Protestants in the U.S. to be a foreign culture.
But still, I’d long forgotten what you just told me. The British would have been suspicious about the possibility of a U.S. alliance with the French. That’s a good point. Thank you. Good learning! I should also have remembered that it’s not a good idea to argue seriously about the War of 1812-1815. Too complicated! ;-)
My #51 contains a link to a good recent book on the War of 1812, and a quote from its concluding paragraphs. But, as you suggest, one book can’t begin to do the period justice.