You have to remember that 1800s France was a danger to itself and others. Having anointed the last century in the blood of its own people, it baptized the 19th in the tears of everyone else. French cannons punched fiery holes in all parts of the globe, and what was done to those holes cannot be described in polite conversation, nor on Cracked.
Mexico at this point had been through so much war that it looked like Officer Murphy five minutes before he became RoboCop. Of course, in RoboCop, OCP spent millions salvaging Murphy, which is way more money than Mexico had, so they ended up handing out IOUs to their creditors. Spain and England, after some grumbling, agreed, because money is good money. France, on the other hand, assumed an attitude toward Mexico not unlike the attitude Red from That '70s Show held toward every other character in RoboCop.
Meanwhile, America was in the middle of this tussle called the Civil War, which, guys, was not civil at all. So the Western Hemisphere's sophomore term was blazing with hazing. Not helping at all was the fact that Napoleon III's France was supplying the Confederate army, since neither he nor President Lincoln wanted to directly combat one another. (But if they did, Lincoln would win, obviously.)
After the Battle of Puebla, it took France a full year to stop wiping its bloody nose, during which time the Confederates lost much French backing. That meant Original Recipe America could focus its efforts on a single gray-clad foe who was whistling Dixie and states-righting itself deeper into a hole.