Wikipedia reads like a blog on this, so I'm not going to be able to go with the easy reference.
Cinco de Mayo is the catchy title for the holiday that, at one point, commemorated the Mexican victory in the Battle of Puebla. The generally remembered impression of the battle is that the Mexican force (rag-tag or formal military, or both) fought off a superior (more numbers or better trained or some combination there-of) French force, at a time when France was the premier continental power in Europe (which, at the least, implies that being beaten by Mexican forces is really not an expected thing). There's lots of places to go with this, but I'm not generally concerned about the exploitation of nationalism by beer companies (if you really want to name yourself after a failed brewer whose major success was in messing up governments, go for it).
The point I'm going to make is really about the rest of history. The army that won the battle of Puebla was eventually beaten (after a siege? quite possibly). In the long-term the French adventure failed. In the shorter term, the heroes of this underdog/against-the-odds battle were killed. By overwhelming superiority, as Napoleon the Third sent more troops into Mexico, and his generals had a good long spat of winning battles.
There should be more here. France invaded a nation because it could, the nations' people fought, and the early heroes died suitably tragic deaths, and the world moved on. Puebla remembers the battle, and that is almost the end of this.
In casual observation, it seems Cinco de Mayo is a Mexican-American holiday in a much different way than it is portrayed. It's a victory against imperialism, which, in the parts of the United States that were once Mexico, has significance.