Imagine that George McLellan, a Democrat, wins the Presidential election through voter fraud (realistic so far, eh?).
He declares an immediate cessation to the war, and withdraws all Union troops to the pre-war Union states. Both sides remain bitter over the war, and especially the South, since the war has been fought primarily on their soil and has caused immense destruction, even by the end of 1864.
Many in the North press for resumption of the war, and private militias are raised for the purpose of harassing the South. The South, nearly broke and trying to rebuild its economy, has no one willing to lend it money to do so (think of the Marshall Plan after WW II). Weakened economically and militarily (which are the same thing, really), it becomes embroiled in multiple defensive actions against the British, who never got over losing their colonies, and who still want cheap Southern cotton for their mills, the Mexicans, who want Texas back, and the Northern private militias.
The South eventually falls, and is split into multiple countries by whomever happened to control the fragments of the territory at the time. This would lead to multiple countries existing in what is now the Continental US, all of them in conflict.
Skipping ahead to WW I, the remaining "US" never enters WW I because it is too small in population and resources to fight in that war, and because of the ongoing conflicts on its own continent. The Germans, in their last push of the war, over run the French / British, and claim a large part of France (primarily Alsace Lorraine) as theirs. Hitler never emerges, and all of Europe eventually fights united against Stalin, but with a much smaller, weaker Soviet Union confined to its own territory (Russia).
Of course, I've left out a few details. :-)
McClellan would have taken office in March 1865. Do you really think the U.S. would have surrendered given where the war was at that time?
Actually, Alsace-Lorraine WAS German; they had taken it when they defeated France in 1871. The French got it back as part of the Versailles treaty in 1918.
I have been to Metz, the Alsace-Lorraine capital, numerous times, a beautiful place; most of the people are of German descent, but French citizens.
After they defeated France in 1940, the Germans took Alsace-Lorraine back. It was liberated in 1944 by Patton’s Third Army, and has been French ever since.