Would it be possible to defeat the Republicans before the Civil War ended ? Even then, could he remain in throne after the US turned their attention to Mexico ?
Then there was no hope ? Uncle Sam would ruin Mexico anyways ?
2) The other problem is that he’s a French puppet just south of the American border. He only survived so long IOTL because he was being propped up by tens of thousands of French troops and the US is in civil war. When the political situation in the US changes it’s unlikely they’ll be willing to put up with a French puppet to the south. Perhaps more dangerously for Maximilian as soon as the political situation in France changes the troops leave and he’s hung out to dry.
Maybe Mexico could use the Franco-Prussian war to break free ?
Break free how? Getting rid of the emperor? Or France? That way they'd lose their only ally.
1. Civil War ends earlier, and Juarez dies
2. US invades in sloppy fashion after regarding the French as violating the Monroe Doctrine, after having gotten cocky; Mexicans heavily defeat early American intrusions
3. the US, unable to do Reconstruction and properly fight Mexico at the same time, signs a white peace
4. the Mexicans credit Emperor Max for seemingly holding off America
profit
If the Americans haven't ousted Max by 1871 they probably don't care he's in power so the alliance with France is pretty well moot. There needs to be a situation in place where the Americans don't see anyone to back against Max so don't bother intervening against his rule.
Maybe Mexico could use the Franco-Prussian war to break free ?
Max will never get the nationalists on side. He’s a foreigner imposed on Mexico by foreigners to act as a puppet for a foreign power. The war is referred to as Mexico’s second war of independence for a reason. He might be able to win the war but I can’t see how he can ‘win the peace’. He just doesn’t have enough support. He’s going to face continuous rebellion in guerrilla form, opposition to his policies from both conservatives and liberals, and the country will still face the extreme socio-economic problems as OTL. I’m certain there’d be another major civil war within a decade and he’ll be deposed when French troops inevitably leave.You could have the McCain-Ocampo Treaty (Or, more usefully, a more pro-American version of it) get through the US Senate and have Emperor Max reject it while utilizing it as propaganda to paint Juarez as a Yanqui toady. If you can egg the man into publicly adopting an Anti-American stance in order to fight for the loyalty of the nationalist intellectuals and domestic merchant classes, it could become politically unpalitable for Washington to support him. Particularly if Juarez or bandits claiming his cause as cover pulls any "propaganda raids" into California during the ACW
You have a very clear point though: by default Max is on charge if there's no challanger. The ball is in those insisting on change's court to present an alternative acceptable to all other parties forgein and domestic... and I don't think the Liberal revolutionaries have a spare
"Break Free" from what? Security, stability, and economic/trade patronage? Because debt forgiveness isen't on the table.