Who did the Mexicans beat for Cinco de Mayo?

The Cinco de Mayo commemorates the Mexican army's unlikely victory over French forces at the Battle of Puebla on May 5, 1862, under the leadership of Mexican General Ignacio Zaragoza. The Battle was important because 4,000 Mexican soldiers defeated a much better-equipped French army composed of 8,000 men that had not been defeated for almost 50 years.