But i think it highly doubtful the CSA would have remained in on epiece. I doubt Texas would take orders from Richmond for too long. The French were involved in Mexico and the texas mexican borders full of unrest. The USA would have been saddled with an enormous debt and nothing to show for it. The USA may not have built the transcontinental railroad, or at least much later. California might have chosen not to be ruled by a greatly weakened debt-ridden north east coast. The Indian wars would have gone differently. The British Canadians may have seized parts of maine and Washington state. The gold rich mountain states and the Mormons may have gone different routes. Alaska may have remained in Russian hands until the Japanese defeated them in 1910. The Mississippi river would be in at least countries with an uneasy peace and contuinuous underlying tensions all along the CSA-USA border.
A broken weakened USA, on a continent divided into hostile countries, would probably not gone to war with Spain twenty years later, meaning no Puerto Rico, no Phillipnes no Guam, no Hawaii, although the CSA always wanted Cuba so who knows what an emboldened CSA might have done. BVut the war with Spain made us a global power. I can't imagine a weak USA with no global interests on both oceans building the Panama Canal.
Would a radically divided hostile American continent have joined with the allies in WW1? Or on different sides? Without the addition of united American might against her would Germany have won WW1? That might also meant have no successful Lawrence of Arabia, completely changing the future of the Arabian oil countries which most likely would have been solidly in Turkish-German hands after WW1.
Without a Roosevelt negotioated peace between Russia and Japan in 1910 would Japan have taken huge chunks of Russia (including Alaska as mentioned above?) Would the rest of Russia have surrendered early to Germany in WW1, and become a German puppet monarchy under the Czar, thus no Communist revolution, no USSR?
That sets a stage for a WW2 with two growing empires, Germany in Europe and the Atlantic, and Japan in Asia and the Pacific with no unified USA to compete with either.
Yes Alan it is all speculation but I have no doubt that a different outcome of the USA-CSA war would have made for a drasticly different future.