To start off, some background about the state of Mexico in the 1860s. Between 1857 and 1861, Mexico experienced a civil war between the Liberals, favoring a more federal state, and Conservatives, favoring maintaining the preeminence of the Catholic church and the military.

The Liberals under Benito Juarez eventually triumphed. However, as wars tend to do, Mexico was facing a economic crisis. As such, Juarez cancelled repayment of debts to European creditors, mainly France, Spain, and the UK. These countries were not pleased with that, so sent a force to take control of Veracruz. Since the US was involved in civil war and Mexico was recovering from one, there wasn't much to stand in their way. However, Emperor Napoleon III of France had designs on taking all of Mexico as a French trade sphere in Latin America, not just the reclaimed debt. When they found out, the British and Spanish withdrew their involvement, leaving Napoleon's forces to march on Mexico. The Battle of Puebla was an early success for the Mexican forces, but the French eventually did fight their way to the capital and install Maximilian as emperor.