The most important historical takeaway from the Battle of Puebla is that when the vastly over-matched Mexican army defeated the seemingly invulnerable French army (which had not suffered a combat defeat in almost 50 years) it virtually guaranteed that the French would not play role in the US Civil War.
Most historians strongly believe that the Mexican government would have taken up the Confederate cause, and that might well have shifted the balance of military power sufficiently to impact the outcome of the war, and thus - dramatically alter US history.
Imagine how things would look today if the United States military was marginalized by a successful sessesion of the southern states, and as a result could not play a major role in the two World Wars of the 20th Century.
Of course, this is all pure speculation, since no one knows if Mexico’s support of the Confederacy would have have resulted in a different outcome, but it might help explain why Cinco de Mayo is observed more vigorously in this country than in its country of origin.
OR - Americans might just use it as an excuse to drink margaritas and Dos Equis.
Go Frogs!