The US and France had already fought once; and in 1811-12, the US was probably within a handful of votes of going to war with France, rather than the UK...
Best,
That's what I was thinking of. Something along the lines of the US is considering war with France, the British "accidentally" let slip they won't oppose an American move against Louisiana, and Congress declares war on France rather than the UK. I remember using something like this as a basis for my first attempt at a TL, and later as a possibility for the US deploying soldiers in Europe during the last Napoleonic Wars (that is to say small number of riflemen as a token gesture).