Well, issues in Europe forced us to abandon the endeavor. Still coincides with the time frame, and French/British intervention in the war (or the expansion of French Empire in the Americas) was a very real threat at the time. I mean, the Habsburg emperor of Mexico (Maximillian I (1864-1867)) was still in power at the end of the Civil War.
Again, given rising issues in Europe (such as Prussian power, particularly after the Austro-Prussian War of 1866), it was wise to leave. Unfortunately, the French troops were defeated in the Franco-Prussian War of 1870-1871, particularly at the Battle of Sedan. So ended the Second French Empire.
As French intervention in the Americas was occurring (such as Mexican Empire), they would not get involved in the American Civil War, particularly due to close ties with Great Britain, which refused to recognize the Confederacy. The French, not seeking to upset their British allies, did not recognize the CSA, essentially dooming it.
Seeing as the intervention lasted from 1862-1867, it would still have been affect at the end of the American Civil War. This being said, I feel France would be a nice nation to add.
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