I think you would actually see a gradual seperation of both the USA and CSA into independent states.
- Certainly the most likely state to break away would be Texas who would be eager to intercede in the French involvement in Mexico (I doubt the rest of the CSA would be as interested in another war).
- New York City might break away from the USA and become a small corrupt nation run by Tammany Hall.
- As slavery becomes less useful/cost effective I can see some of the CSA states doing away with it and others hanging on. Just as this created a problem with the Northern states it will create problems between the CSA members and you would see further seperation.
- The issue of women's suffrage would almost certainly create problems and division as the 19th century winds down. Some states would accept it, others would not.
- Just as problems/wars occur between European nations I think you would see them occur between American nations.
- With the rise of Communism a few American states would likely adopt it as a form of government (Minnesota seems like a likely early adopter).
- I suspect WWI would happen without much American involvement ... meaning it would drag on longer and be bloodier but likely would end with the same result.
- The Nazi's still come to power in Germany, the US is slower to intercede, the Japanese dominate the Pacific, there is no Manhattan Project, and the overall international influence of the Soviet Union is greater.
When all is said and done if the North loses the Civil War I don't think we have a happier or more pleasant world. A United American state has been a much greater force for Good in this world than it would be if it were divided.