Plausibility Check: A House Forever Divided

American Civil War TL's have been pretty much overused, I know, but here's one possibly unique scenario.

The year is 1863, and the Confederate cabinet under President Jefferson Davis orders Robert E. Lee to carve up a portion of his Army of Northern Virginia and send it west, to help the outmatched western Confederate forces in the Siege of Vicksburg. Thus, the plans for an invasion of Pennsylvania were dropped, as Lee was more focused on fighting a purely defensive war up north.

The southerners narrowly defeat the Union forces outside of Vicksburg, and go on to delay any northerner advance on the western fronts for quite a few months, after the Union would lose again to the Confederacy at Chattanooga. However, by late 1864, the Union would have reopened the western front, outnumbering and outgunning the Confederates once more. Eventually, the southerners' defence would have finally been cracked in the west, as paranoia engulfed the Confederate leadership, who ordered the remnants of their army to begin offensive campaigns in Pennsylvania, the Army of Northern Virginia included.

By February 1866, the Confederates are destined to lose the war in a short amount of time. However, diplomatic meddling from the British and the French lead to a peace treaty being quickly signed, with the Confederacy surviving as a national unit, albeit narrowly (with just five states composing it). The Union goes on to become a superpower as it did IOTL, but the CSA continues to exist as a banana republic well into the 21st Century.

Plausibility check?
 
Plausibility check; implausible. If the union can reduce to Confederates to 5 states, and it's 1866, even French and British "meddling" (do they have a reason?) won't stop reelected Lincoln and company from beating the Confederacy entirely.
 
Question; why would the UK and France suddenly side with the (presumably) rapidly disintegrating beast that was the CSA?
 
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