What was the name of the French-backed Mexican empire established after France captured Mexico City?

The Second Mexican Empire was the French-backed Mexican empire established after France captured Mexico City.

France invaded Mexico during the 1860s and eventually occupied Mexico City. Napoleon III then supported a monarchy intended to extend French influence in the Americas. Archduke Maximilian of Austria accepted the Mexican crown and became emperor in 1864, creating the Second Mexican Empire.

The empire was opposed by Benito Juárez’s republican government and by Mexican resistance forces. France eventually withdrew its troops, in part because of pressure from the United States after the American Civil War. Without sustained French military support, Maximilian’s regime lost power. He was captured and executed in 1867, and the republic was restored.

The name can cause confusion because Mexico had an earlier monarchy under Agustín de Iturbide after independence. That earlier regime is called the First Mexican Empire. The Second Mexican Empire belongs to the later French intervention connected historically with Cinco de Mayo.