The French began mucking around in Mexico in 1861, because the United States had more pressing matters to attend to than to get froggy about a violation of the Monroe Doctrine.
Despite the victory and despite heavy guerrilla resistance by Mexican patriots, the French were able to set up a puppet regime in Mexico. By 1866, with some realization that the United States now had the largest navy and the most battle-hardened army on the planet, the French began to withdraw. The United States helped things along by "losing" arsenals of weapons to the Mexican resistance.
For some reason, the French puppet emperor of Mexico, Maximilian I, didn't flee. He was captured, given a trial by court-martial, and, along with two of his generals, shot by a firing squad on June 19, 1867.
Max is on the right side.
The story was that Maximilian paid the firing squad not to shoot him in the head, so that his mother could view his body after he was embalmed and sent home. They kept to the bargain.
The generals died shouting "long live the Emperor". Which was sort of futile, as they shot Max first.
Anyway, today isn't supposed to be a day for stupid Anglos to get wasted. That's St. Patrick's Day.