Imperial EarthThis alternate starts with the Confederate States of America receiving much stronger support from Britain because the crop failure in the European wheat crop from 1860-62 never happened, thus removing British reliance on importing Union wheat. The Confederate Army, with better supplies of arms and food along with training, fight the Union to a stalemate. They achieve sovereignty, and the Union abandons the War as too costly. One interesting thing that happened during the war was that during the Union siege and blockade of New Orleans, the Mayor of New Orleans asked the French for help in lifting the siege, and a small French fleet breaks the blockade and French troops reclaim New Orleans as French territory.
After the war, the Union's nose is bloodied and the National Ego is bruised. The U.S. loses its expansionist fervor, and turns inward. It never becomes the world power it did in our parallel. The U.S. stretches from the Atlantic coast to the Mississippi River. The vast expanse of the Louisiana Purchase is never heavily settled, and the Indians and what settlers there are strike a peaceful deal, since the settlers know there won't be any cavalry coming over the hill. Alaska remains in Russian hands.
Texas resumes its secessionist tendencies after the Civil War and leaves the Confederacy to become its own nation. Several border clashes occur between Texas and Mexico. A truce is settled and Texas and Mexico eventually form an alliance. Mexico keeps its original holdings in the Southwest and becomes a much more powerful regional state than on our timeline.
The forces that led Europe to World War I still exist. WWI arrives on schedule, but after the intense clashes of October, a hurried peace is made, ending the war but resolving nothing. The consequence of this is that the Great Empires of Europe never fall: Czarist Russia, Germany, Austria-Hungary, the Ottomans are all still around, as well as the British and French, conniving and scheming against each other.
This is a politically very interesting place to be. Lots of intrigue, diplomacy, espionage, etc. You've got multiple North American nations to deal with and Europe is very interested in the New World.
I created a GURPS character in this world: Jacques Devereux, Agent of France.