In order for the confederacy to win, it would require either outside intervention or a g-dsend. I'm gonna go with the former.
Considering the British in OTL were very close to personally marching into the south and backing the confederacy, along with invading from the north and blockading American ports/breaking the American blockade, you have a future where the US and Britain are pissed. If Britain invades from Canada, they'd likely go straight for New York where two Russian fleets are waiting to fight the British and French due to an uprising in Poland and the Ukraine.
Considering France was right next door in Mexico at the time, and the US was supporting the Mexican republicans/liberals against the Mexican Empire and its foreign sponsors France and Austria, the Franco-Mexican war and ACW could link up.
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The CSA would likely get Texas, Virginia, both Carolinas, Tennessee, Alabama, Georgia, Louisiana, Mississippi, Florida, Arkansas, and the Indian/Oklahoma territory.
Referendums would take place and fail in Kentucky and Missouri. Virginia would lose West Virginia (likely in a referendum) and its territory on the Delmarva peninsula.
France would demand a lease on New Orleans, Britain would want a lease on a Florida port like Tampa or Miami. They'd want it close to the Caribbean. This would piss off certain states seeing it as a breach of their sovereignty.
Britain and France, abhorring the practice, would demand an end to slavery. Considering the South claimed (falsely) that the war was fought the most over states' rights, and slavery just happened to be a small extension of said rights, the CSA would look hypocritical if it made too big of a deal over slavery. Sharecropping, segregation, serfdom, and living as second class citizens would become the replacement. Still, the slavery issue would create further tensions in the new Confederacy that would weaken the union as a whole.
The CSA would next lose some of its less devoted members, chiefly Texas. Considering the war was fought over the right to secede, once Texas pays off its debt it is going to milk that cow for what it's worth. It may claim portions of Oklahoma/Indian territory. The neutral strip is likely a given that Texas would take with ease.
The next state to break off would likely be the Indian/Oklahoma territory if Texas doesn't take it. Let's refer to it as Sequoya. Sheer ethnic and cultural difference would be the pretext. It may or may not join up with Texas willingly or forcibly, though it is unlikely that Texas, still getting its footing, would make such an aggressive action so quickly.
Of the 10 remaining states, the two Carolinas may break off as a bifederal state. They could declare they are doing so out of fears of state and national sovereignty being taken away by the British and French.
Virginia, now isolated with the secession of north Carolina (the Appalachians form a barrier separating Virginia from the already short Tennessee-Virginia state line) would just end up being absorbed by its massive northern neighbor. Virginia was already the most northern like of the southern states anyway, except for a few pockets around the south like New Orleans.
The US would want to be able to push down the Mississippi, and France would try to push its influence up. Arkansas would be taken by the United States, and Louisiana would be partitioned. Everything west of the river goes to the US, everything east would go to France.
The Florida panhandle, Mississippi, and Alabama would end up as one separate federal country with its own cultural sphere separate from the wealthier and less mountainous and more developed Georgia, and the more rugged cowboy like Florida. The territories of former west Florida in French Louisiana, and the appalachian regions of Georgia would come along for the ride.
The remaining two states (Georgia and Florida) would most likely end up as British a single bifederal British protectorate.
Considering the US would resent Britain and France, and likely have a stronger relationship with Russia and perhaps Prussia/Germany, the US will eventually take the British and French territories. Texas will either be taken by the United States as a vassal state or an annexed territory to be partitioned. Or on the unlikely side Mexico could get frisky and take a small portion of Texas.
If Sequoya joins Texas it gets annexed/vassalized. If it doesn't it definitely gets either conquered, or lobbies to join the US because otherwise it'll end up an economic backwater.
The Carolinas coastline, ports, and cities will be too tempting for the US to not Vassalize, domintate, and later annex.
The Redneck riviera nation will realize that without anything going for it, its really screwed, so it'll try to rejoin.
US efforts to challenge France and Britain in coordination with Prussia/Germany, Russia, and likely Italy will probably help it conquer portions of Canada (BC up to the 52nd parallel, the Maritimes, upper Canada, Newfoundland, Labrador, Quebec, PEI, Manitoba, Alberta, and it may try to establish a port on Hudson's bay). It will take more populated, more productive regions, while the rest of Canada will remain very much British.
The US will likely try to take the Bahamas and Bermuda too.
The US will likely accept North Borneo and Santo Domingo as states/territories. Without the South's more isolationist/racist votes in the Congress to muck things up, they'll pass finely.
Eventually the US will rack up enough to buy Alaska, the Danish VI, and it will likely try to purchase Baja California, Sonora, and Cuba. Spain won't sell Cuba, but a weakened and indebted Mexico may make a deal.
The Spanish-American war will likely start even earlier due to the US and Spain fighting in the far east. American North borneo and the Spanish Philippines being neighbors, things will get hostile. The US, being more expansionist and ideologiacal without the southern culture holding it back, may take the entire Spanish empire for itself: The Marianas, the Caroline Islands, the Marshall Islands, Spanish Guinea, Spanish Seharra, Puerto Rico, and Cuba. Spain will only keep the Canaries and Ifni.
Spanish African territories will make excellent US west Atlantic ports. Low population in said territories will make immigration easy. The US will likely try to vassalize Liberia, and perhaps annex it.
Morocco always had good relations with America. It was one of the first countries to recognize it. With an American colony just to the south, Morocco will be protected by America and France will not not be able to take over the country. Amero-Moroccan trade will be strong, and immigration will likely kick off earlier making a less Islamaphobic America. Spain may end up taking Spanish Morocco though.