France still loses and Maximilian gets shot.
It's just a temporary setback.
I agree. The Battle of Puebla wasn't even that decisive of a battle. France hadn't abandoned Maximilian yet, and when they did it wasn't because the lost this battle but because they became engaged in another war against Prussia. Unless they are doing, ASB-well in Mexico the French will drop the project and abandon Maximilian.
The reason the battle gained the prominence it did, was because Porfirio Diaz took part in it. It was perhaps the battle that originally made his name. When he became President of Mexico he overstated the importance of the battle and made it a celebration.
How it gained the prominence it did in the United States is one of the things of OTL that seem to come out of nowhere. Today, in Mexico (outside the heavy tourist spots and Puebla) not much attention is given to the date at all.
And even without Cino de Mayo, sorority girls would find an excuse to drink (it just might not be based around tequila) since it is basically just a celebration to kick start the summer.
In conclusion. Not much changes.