WI Franco-American War 1861

Suppose, for the purpose of discussion, that someone other than Lincoln was elected TTL (Seward, perhaps?). I've heard that the American population was greatly opposed to the French intervention in Mexico, but couldn't do anything about it because of the Civil War. So, what if the Civil War was averted, and the USA declared war on France (and maybe other members of the invading coalition, i.e. Spain or UK) and then deployed the US army south of the border to defend the Republicans in Mexico. How would this war play out? Would Napoleon back down? If not, how would the naval war go, along with the one on the ground?
 
Indeed, the Mexican government even pleaded for American support, and America would have answered positively if they were not in civil war. But I don't think that without a civil war the French would have been so keen on intervantion in Mexico.
 
Like Orko said, I don't think that the French would intervene if the US wasn't in a state of Civil War. The fact that the nation that considered itself the "Big Brother" of all nations South of it was busy killing itself, was one of the big reasons why France decided to invade Mexico.
 
Would they still go for a blockade? After all, Mexico did just cancel all of its debts to the powers in question. Maybe they were trying to use the Monroe Doctrine to their advantage and just drop the debt?
 
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