By blocking the march to Mexico City, the victors at Puebla set back Napoleon III´s conquest of Mexico and the installation of the Hapsburg archduke Maximilian on the “Cactus Throne” by at least a year. Had French soldiers reached the Rio Grande in 1863 rather than the end of 1864, Napoleon might have been in a position to offer recognition and formal alliance to the Confederacy.
Napoleon made clear in the summer of 1862 that checking the United States’ influence in the Americas was a primary concern of his venture:
The prosperity of America is not a matter of indifference to Europe, for it is the country which feeds our manufactories and gives an impulse to our commerce, We have an interest in the United States being powerful and prosperous, but not that she should take possession of the whole of the Gulf of Mexico…and be the only dispenser of products in the New World.
Admittedly, there’s a bit of the speculative in there, but it was not outside of the realm of possibility, either, and adds extra transnational significance to the date.