It is relatively common knowledge (I believe) that Spain was in support of the C.S.A. with Prime Minister O'Donnell being probably somewhat more vocal of his support than Isabella. Still, Spain was
not a fan of the U.S. at the time anyway and very nearly took steps to support the Confederacy, if only in recognizing her.
It's not like it was unpopular in Europe at the time.
Maybe Britain stays out of it as in OTL but France and Spain do not. This may have the potential to combine an early Franco-Prussian War and an early Austro-Prussian War if Prussia goes to war with a Franco-Austrian alliance at the same time as Spain and France are at war with the U.S. who calls upon assistance from Russia and receives it.
If I'm not mistaken, this puts a
U.S., Russian, Prussian/German States, Italy
Against a
C.S.A., France, Spain, Austria.
Correct me if I'm wrong there. Depending on how it goes, I can actually see Britain eventually siding with a victorious U.S., Germany, Russia - at least post war. The Treaty would be signed in London as Britain remained (mostly) neutral.
If the U.S. loses... well that's something else entirely.
Throw the tomatoes at all that if you want, I'm tired. Just make sure you remove them from their cans first.
EDIT: This seems to be a culmination of much of this discussion, anyway. I'm fairly proud of it. I'd really like to work on something like this at some point if there's any interest. I'll have a lot of restless nights of research to put in and I'll need a little help, but I've got some ideas.