1870 U.S. vs French Empire & Hasburg Mexico

Assume the following:
  • ACW happens as IOTL.
  • Maximilian wins in Mexico.
  • France wins the Franco-Prussian War.
Now, Napoleon III wants to expand his empire in America and sets his sights on the small central American republics. The USA doesn't like this and wants to kick off the French from Mexico.

Can the US take out Hasburg Mexico and the French imperial forces? Also what would be Britain's position?
 
For a U.S. only 5 years removed from the Civil War I'd say yes though the domestic reaction to going back to fighting probably wouldn't be very positive. Personally I think Britain would remain neutral but closer towards the United States. A powerful French Empire is something Britain would prefer to contain especially since there's no unified Germany to keep it in check.
 
Does France attack the U.S. or launch any directly aggressive moves? That could make a huge difference.
 
Assume the following:
  • ACW happens as IOTL.
  • Maximilian wins in Mexico.
  • France wins the Franco-Prussian War.
That's a pretty big gap between the first two points and the third. The United States would not have spent 5-6 years doing nothing while a French puppet sits on the throne in Mexico, especially since they had the largest and most experienced army in the world at that time. If, in the years after the Civil War, the French persist in Mexico despite the United States' threats (which Napoleon III would have brain dead to do given the campaign's growing unpopularity at home), the United States would have intervened and toppled Maximilian in short order. Consider that, at the height of the French occupation of Mexico in 1863, the French Foreign Legion was less than half the size of the Army of the Potomac alone (39,000 to over 100,000, respectively). In total, the United States had over 600,000 well-equipped and battle-hardened troops at their disposal by the end of the war. France would have had no chance against such superior numbers, especially when growing tensions in Europe would have forced the French to withdraw troops from Mexico.

After the Emancipation Proclamation, the United States was immensely popular and would have been supported by virtually everyone in Europe outside of France - especially by the British, who I'm sure would have been very excited to see their ancient rivals getting thrashed in an overseas venture.
 
I think Mexico would be defeated just as easily in 1870, as it did during the Mexican- American War. For the US to defeat France, the US would probably begin by seizing all remaining French colonies with in North and South America. This would immediately demoralise the French and would fan the flames of dissent with in the Empire. All the US has to do to defeat Napoleon III's Empire is to make the emperor look increasingly weak. GB may enter the conflict, if only to take French colonies in Africa and Asia.
 
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