How about North German Federation + Italy + Russia on one side and Austria + France + Ottomans on the other? UK finances everyone and maybe prunes a few colonies in the process, US makes a nice post-ACW economic recovery while maybe ex-Confederate soldiers find work as mercenaries, sort of a "lost legion" concept?
Maybe the war backfires from its original purpose and leaves a united South German Federation (Greater Bavaria in all but name perhaps with German Austria) under British protection, a remaining French Empire under the son of Napoleon III, a Prussia that takes Bohemia and Moravia while perhaps Hungary goes free with a titular Poland out of former Galicia. Italy gets Venice and Rome, probably not Corsica or Tunisia, and Russia takes Wallachia and Moravia while making plans for Bulgaria and Kars. France survives only due to British aid and then as a mean of preventing Communism from taking root while the Ottomans enact reforms that may or may not work. All the while the US sits it out and Spain buys back a random colony or two at discount prices because they can. Would Japan be offered a chance to buy Samhain or Kamchatka under these circumstances and how would China or Africa be affected? Does South Africa unite earlier and expand farther if they can take foreign territory on their own or do the Boers go deeper into the continent found a lasting nation in OTL Mozambique or Botswana?
Worse Long Depression, mayhaps WWII analogue coincident with/in place of the Scramble for Africa?
What would be really interesting then is if there was either more explicit French jickijackery during the ACW (perhaps Puebla goes sideways for the defenders, and Mad Max's empire gets better established earlier allowing it to be used as a platform for French assistance to the Confederacy) or more explicit Prusso-Russian support for the Union cause, or both, which would put the United States very much on the anti-French side in the next conflict...