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I'd like to analyze what butterflies could be created if the French intervention in Mexico had been successful and the Juaristas had been defeated some time before the black decree circa 1865 which thus leaves the 2nd Mexican Empire intact. Also lets say in TTL the US does not somehow try to overthrow the 2nd Empire immediately following the defeat of all the Confederate generals left after Lee's surrender.
I'd especially like to consider what would the initial and long term effects of this would be in Europe. As I understand it most on this site believe that a French success in Mexico would prevent the Franco-Prussian war by making Napoleon III's reaction to the Em's Telegram less aggressive. I'd like to discuss this further but I'd also like to consider how it could changes things such as the austro-prussian war before that since Maximilian I was from the ruling family in Austria and settling him as Mexico's ruler might affect the way the austro-prussian war is managed.
I have a specific POD in mind for how the Jauristas are defeated but I don't want to share that until some others have posted so as to not spoil any fresh ideas.