1862 minus 50 years equals 1812.
I seem to remember Napoleon's disasterous retreat from Moscow, many losses against allied troops including losing Paris, being exiled and then coming back to lose one last time at Waterloo. But other than that the Mexican students' grasp of history is pretty good.
I propose celebrating April 10th as another fraternity drinking holiday to celebrate the coronation of Emperor Maximillian.
You remember correctly. Note that the Wikipedia page on the battle (take it for what it is worth) gave a strength of 6,500 for the French versus a 4,500 strength for the Mexicans. While they were outnumbered the advantage (3:2) was not necessarily decisive. The terrain also played a significant part in strengthening the Mexican position.