We should all celebrate today. If the Mexicans hadn't defeated the French at the Battle of Puebla there probably would not have been a USA as we know it.
I serious doubt that, because in 1865 the French were still contol in Mexico (see below), the United State had the biggest standing army in the world with th Union and former Confederate troops were ready to help the Mexicans kick out the French to regain their country's government and the US restoring their principle of Monroe Doctrine.
The Battle of Puebla was an inspirational event for wartime Mexico, and it provided a stunning revelation to the rest of the world which had largely expected a rapid victory for French arms.
Slowed by their loss at Puebla, the French forces retreated and regrouped, and the invasion continued after Napoleon III determinedly sent additional troops to Mexico. The French were eventually victorious, winning the Second Battle of Puebla on 17 May 1863 and pushing on to Mexico City. When the capital fell, Juárez's government was forced into exile in the remote north.
With the backing of France, the Habsburg Archduke Maximilian became Emperor of Mexico in the short-lived Second Mexican Empire. "Some have argued that the true French occupation was a response to growing U.S. power and to the Monroe Doctrine (America for the Americans). Napoleon III believed that if the United States was allowed to prosper indiscriminately, it would eventually become a power in and of itself.
The French were going to supply the Confederates in the Civil war. The defeat at Puebla prevented the French from aiding the Confederates. Thus the North was able to be victorious at Gettysburg. If the French had been able to supply the South, the Civil war would have turned out much differently.