I'm planning a TL at the moment and I need a reality check on something. Through a set of PODs that really take off in the 1830s within the US, the US goes into Mexico and takes a larger chunk of it. Basically everything that would had been US in the long run aka the Gadsden Purchase and Mexican Cession, and OTL Northwest and Northeast Mexico. Yes I know that cuts a shit load of Mexico and makes it American.
But anyhow, the French still go into Mexico after the ACW breaks out under the same thing they did OTL. With out the northern part of Mexico to run, could France get Mexico to the point that Maximilian's rule in Mexico would be stable and fully defeat Republican forces in Mexico?
Assuming all that extra territory captured became slave states (due to the Missouri Compromise), why would the South feel the need to secede like OTL? They have more congressmen and senators on their side, so they wouldn't fear free soil and abolitionist politicians as much.
It could lead to rising liberal sentiments rather than weakening them. Benito Juárez became president not long after Santa Anna was overthrown. After all, they could blame him for the disaster of the OTL Mexican War.
The French intervention that put Maximilian on the throne was a plan of Napoleon III to counter British influence in the Americas. Such a POD could mean he never gains power in the first place. However, there were still monarchists in Mexico, so maybe someone else gets the same idea? It's not like Mexico is in much of a position to stop an invasion in its ATL shabby state. There were monarchists in Mexico during and after independence. Remember that they tried to get a Spanish prince to become a constitutional monarch under the Plan of Iguala, but none would accept the offer.
Mexico would also lose significant parts of its economy. One of the conditions France imposed on Mexico was a lien on the mines in Sonora, which would be taken by the U.S. in ATL.
See
The Penguin History of Latin America and
Maximilian in Mexico A Woman's Reminiscences of the French Intervention 1862-1867 for more info. Both have Kindle editions, and the latter is free.