Picture it.
The year is 1867. Under the driving initiative of Emperor Napoleon III, the Second French Empire has been supporting the newly created Empire of Mexico since 1864. Ferdinand Maximilian Joseph of Austria rules in Mexico City under the name of Emperador Maximiliano I, supported by a French army and his own local supporters. Volunteers from Belgium and Austria are also present.
Following the recent end of the American Civil War, the United States has begun making plans and statements concerning the situation in Mexico. General John Schofield has been sent to France to seek withdrawal of French military forces from Mexico immediately. U.S. Navy forces have been deployed to block possible landings of French reinforcements for General François Bazaine and the French troops already there, and General Philip Sheridan is in Texas overseeing the movement of U.S. military supplies to the Mexican Republicans in Chihuahua, as well as overseeing some 50,000 U.S. troops.
President Andrew Johnson, at this stage, has shifted U.S. policy from polite sympathy of the Republicans to open support and threats of force.
In reality, the French chose continued Franco-American relations and backed down. Republican forces won the war, and Maximilian was shot. Here, however, we have a departure from reality.
While in France about his mission, General Schofield comes to believe Napoleon III is stalling for time. He believes he has evidence the French are gathering a larger force to send across the Atlantic to Mexico, hoping to brush back the U.S. blockade and reinforce General Bazaine, weakening the American and Republican positions. He leaves Paris at once, intent on returning home with his news.
Upon his return, President Andrew Johnson is concerned. He has heard nothing in the reports from General Sheridan in Texas which indicated French preparations for a withdrawal. General Bazaine and his men are still reported by reliable sources to be in Mexico City. Having made up his mind, he sends his orders.
Within a few days of receiving the President's instructions, General Philip Sheridan marches south at the head of 50,000 U.S. troops in three corps, heading south into Mexico to rendezvous with Republican forces. He will then head south, and march on Mexico City in the hopes of defeating the some 40,000 French troops under General Bazaine and their Mexican allies in pitched battle before French reinforcements can arrive. Within days, a message reaches Bazaine and Maximilian in Mexico City.
What happens next?