Dixieland1861
Banned
While there was some Romanticism for the Confederacy among the British Aristocracy, including the Queen's-Consort, the majority were firmly anti-slavery by the 1860s, especially the working classes, whose influence was growing. Throw in industrialization, and you're right, the North in Britain's natural ally. (The British were never going to recognize the Confederacy, short Lincoln invading Canada for no reason during the middle of the war, see A World on Fire; Britain's Crucial Role in the American Civil War) As far as who becomes President in the North, I have no idea, but there will be no Reconstruction and no Lincoln Assasination, so that effects politics. Settling the west will be a big issue. I could see the North trying to get even more immigrants to block the South in to the west with homesteaders, which will effect politics even more, perhaps even in Europe. Imagine the U.S. Government subsidizing immigration costs as part of its national security strategy.
Anyways, I imagine there will be a great power war. But a part of me also thinks that a USA/CSA split is just inviting the concept of proxy wars and economic imperialism get an early start as well. Some enterprising young diplomats in Europe might see that economic potential of the Americas could be just as valuable a bauble, probably more so, than colonies in Africa and Asia, or even certain pieces of Europe.
Well, I certainly in agreement that a USA/CSA split would cause proxy wars and economic imperialism that would interest the Europeans, but when I said Britain wouldn't automatically become allies with the Confederacy even if they recognize them and be neutral towards both the Union and the Confederacy I mean that Britain would just simply trade the two without aligning with either side (though that would change in WW1 and WW2 when they as you said ally with the North) after all some British did meet the Confederates or witness battles such as Gettysburg and the Confederacy would want to offer as much cotton to Britain as they could as well as (like you said) get young diplomats in Europe and that country interested in the Americas and perhaps allow them to invest business there. For who would become president of the United States if the Confederate States won the Civil War the timeframe of 1861-1863 (or to a lesser extent by some such as Anaxagoras 1864) was the years the Confederacy could have won there's the Trent Affair gone wrong for the Union resulting in the British siding with the Confederacy, General Robert E. Lee not losing Order-191, Shiloh being a (pyrrhic) victory for the South (if Johnston had stuck with his original plan to organize the troops in linear fashion and drive enemy Union troops into the swamps or weather didn't delay them) or Albert Sidney Johnston actually getting the tourniquet applied to him thus saving his life for another battle with Ulysses S. Grant (I highly recommend you read the book Dixie Victorious written by former U.S. Military Lieutenant Peter Tsousas and other war historians that cover all 10 possible Confederate victory scenarios) well's there the 1864 presidential election where Abraham Lincoln thought he never get reelected now imagine if one of those scenarios above had happened the Democrat candidate was former General George B. McCllelan and he would have won the election had he been in elected. On the topics of immigration and homesteading, I think I would agree with you that such a policy by the Union would certainly happen but there is still issue with having hundreds of thousands of non-Anglo-Saxon immigrants in America just to be used to block Confederate westward homesteading as there were still nativist, anti-immigrant elements that existed that would have objected to this plan.