Some constructive criticism on the idea of a Britain/France/US alliance. First some stuff I dislike about it, and my reasoning, second some advice on how to make it better.
The whole reasoning behind their potential (but probably very unlikely) military support of the CSA was to weaken the United States. They basically saw an uppity nation espousing radical ideas, and it was a threat to their interests. Supporting the CSA would both weaken the US and help create a balance of power. Getting into an alliance with the US completely defeats that purpose. By propping up the weakened US, they're just putting it at a better position to damage their interests. The leaders of France and Britain are not stupid enough to think that an alliance will ultimately keep the US docile. Economically, both nations were strong enough on their own and with normal trade. They might get a little bump from beneficial trade treaties, but not much. For military, the US is largely useless. What threats are there in the region? Canada is British, Mexico is a French puppet, the CS really isn't strong enough to do much damage to the European powers. America's conscript military just wasn't equipped or capable to prove a decisive factor in European wars.* In actuality, it's more likely the US would just drag Europe into a second Civil War. And, hell, once the US+Britain+France win that and the US reabsorbs the South, what have the European powers gained? A strong regional threat that's placated... for the moment.
As for America's point of view, there's no way in hell they'd agree to an alliance. America's global isolationism was still in effect. Washington's "no foreign entanglements" was still remembered by most of the US. America was suspicious of getting involved with Europe. The idea of America and Europe working together to make the world a better place is really a post-WW2 creation. And especially Britain and France in a timeline where those two nations just intervened in a bitter war on the opposing side. Could you imagine Osama bin Laden coming out and saying "Hey, we should be friends with the US now! Sorry about the whole 9/11 thing!" That's not to say a US alliance with either of them isn't in the cards decades in the future, but only about a decade after the end of the war?
First recommendation: Britain and France don't get directly involved with the war. Helping bust the blockade, sure. Economic assistance, sure. But direct assistance is a bit much.
Second recommendation: With Britain and French direct intervention removed, try a different POD. Think about different possibilities for the CSA to win the war. Think more incompetent Union generals. Some idiot Union general moves into Kentucky before Bragg does, pushing it into the Confederate camp? Maybe a more successful Maryland Campaign? The Democrats win in '64 after strong Confederate campaigns? New York and Pennsylvania weren't overwhelming Lincoln victories, and they'd turn the lopsided 212-12 electoral vote to 153-80. Still pretty one-sided, but combined with a few other changes and failures of the Union military (same general that fucked up Kentucky leads to a relative Midwestern stalemate, instead of the entire Mississippi being captured?)... I'm just babbling here to give you some inspiration. Take a look at some of the things I've said, check out what you think of them and their possibility. Use any or all of my suggestions here if you want. Better yet, take your own look into them, and figure out how to make them as plausible as possible instead of just a bunch of random PODs.
Third recommendation: So, you've removed Europe from direct intervention, and have still found a way for the South to win the war. Hurrah! Next step is getting that pesky alliance. See, a lot of things I've said still apply. But after the war, it's possible for the US to go one of two ways: having had a major military embarrassment, it holes up. The people become isolationist and don't want to intervene in foreign conflicts. Or, having lost a lot of territory and a major wound to national pride, a charismatic and aggressive leader decides to bolster patriotism through foreign adventures and supporting
filibusters. The US isn't going to be ready to move onto the latter for a number of years, but given time, it's definitely possible. From there, it's up to you. Take a look at the end of the Second Mexican Empire. It's a natural diplomatic meeting point for the US and France. How can you use it to make them friendly? That's up to you.
Fourth recommendation: Research, research, research! A good timeline does not come easy. It's not a simple matter of saying "Wouldn't it be cool to see American troops fighting in Bavaria during the Franco-Prussian War?" If you want a timeline to be good and accurate, be prepared to research. This can be as simple as looking things up on Wikipedia and poking around the internet or as complex as devoting the majority of your free time to a single timeline (see Jared & Decades of Darkness).
I think that's about it for now. Good luck!