I think the holiday is now celebrated more in the United States than in Mexico. But that is probably appropriate. The day celebrates the defeat of the French Army against a numerically inferior and more poorly equipped Mexican Army. The geopolitical consequence was to keep Napoleon III out of North America, and also prevented the French intervening on the side of the Confederacy. So it is no small irony that the reason the Union remained intact is thanks to 4,000 Mexicans who never considered, on May 5th, 1862, that they didn’t stand a chance against a French army twice its size.
Nevertheless, the French ultimately prevailed in installing a puppet government in Mexico, but after the end of the American Civil War, the United States was able to provide assistance to the Mexican liberals to expel the puppet government, thus ending monarchy in Mexico. So today is a day you can drink to Union, the eventual end of monarchal rule in Mexico, and a French military defeat. I can drink to that.