Confederate strategy.

[Saphroneth]

Actually the Mexican Civil War had French troops and the first Foreign Legionarires. Shortly after the Civil War the Johnson Administration made it quite clear that the French needed to go back home. Do no the Mexican Civil War of the mid 19th century had plenty of foreign involvement.

I fear there's a misapprehension. The Mexican Civil War was the Reform War, 1857-60.
The French intervention in late 1861 and onwards was actually a separate incident leveraging non-payment of debts (and grew out of a trilateral intervention by the British, French and IIRC Spanish), and essentially amounted to an invasion once the other two left - which kicked off a "second civil war" of sorts because the losing side in the Reform War threw themselves behind Napoleon's picked Emperor candidate, Maximilian.
It's roughly equivalent in timing terms to a British invasion of the US in 1866 over Fenianism - it wouldn't amount to intervention in the Civil War, the Civil War would already be over and done with by the time the invasion arrived!