Quite frankly, at the time Mexico wasn't fit to occupy a post office, much less any territory belonging to the United States. Mexico had just come out of the Reform War, which was a four year civil war that left Mexico's infrastructure and economy severely damaged. The whole reason the French intervened in the first place(or, at least their casus belli) was because Mexico had suspended its payments on foreign debt.

And the French didn't simply 'attack' in the 1860s, they invaded(with British and Spanish backing) in December 1861, and took the capital in May 1863. The French spent the next two years consolidating their victory and installing Maximillian as Mexican Emperor. When the US Civil War ended, the United States started pressuring France to withdraw from Mexico, and France decided that relations with the United States were more important than maintaining Mexico as a puppet empire, and withdrew in 1866. Maximilian was overthrown and executed the following June.

Not only that, but the border territories of the US weren't undefended at the time. There were conflicts in Arizona and New Mexico territories between Union and Confederate forces, and the United States kept troops in the West to protect settlers and interests from Indian raids.

Finally, even if Mexico had been united, there was no illusion that once the American Civil War ended, the victorious power wouldn't turn its attention back to Mexico. The United States would never and could never have allowed the theft of its territory, and it had soundly beaten Mexico not even two decades previous. If the Confederate States won, their ambition was and always had been to expand slavery, and the western border states would have been their first targets, being further from Northern centers of power and bordering Texas. In fact, though it wasn't known at the time, some Confederate leaders had plans to expand south after the war and annex Cuba and Mexico