Final answer:
The Battle of Puebla on May 5, 1862 was the first major battle when the French attacked Mexico, which is commemorated as Cinco de Mayo.
Step-by-step explanation:
The first battle when the French attacked Mexico during Napoleon III's intervention in Mexico was the Battle of Puebla on May 5, 1862. Although the French fleet took Veracruz in 1861 and planned to capture Mexico City, their advance was halted at Puebla where they faced a major defeat at the hands of the Mexican forces. This event is commemorated annually as the Cinco de Mayo holiday in Mexico and the United States.