The holiday of Cinco de Mayo may be somewhat like Christmas or Memorial Day in that for many celebrants it's lost its connection to the original event, but as wargamers it's good for us to note that May 5, 1862 does represent a really remarkable victory for a force of militia against regular forces.
This site has a lot of details but I think the most remarkable fact noted by the author is not the numbers engaged (about 6,000 French against 4,000 Mexicans) but the fact that the French were armed with rifle-muskets while the Mexicans had regular smoothbore muskets. These rifle-muskets were the same weapons that supposedly made American Civil War combat so deadly, yet here was the French who suffered the higher toll. More than 400 French were killed, compared to just 83 Mexicans. While it's true that the Mexicans had the benefit of a trench and forts, one wonders why the French didn't take advantage of the superior range of their weapons. (they also had rifled artillery, where it appears the Mexican guns were smoothbores.
About the only explanation that comes to mind is that it was sort of like Bunker Hill -- the French might have thought they needed to demonstrate that the rag-tag militia opposing them could not stand against their high-quality troops. And like at Bunker Hill, or New Orleans, this turned not to be true. The militia was sterner stuff than expected. In this case it appears that much of the Mexican militia was made up of combat veterans. In any case they won that day decisively.