The Confederates were never intending to annex the rest of the country, they just wanted to break off. At most, they would've taken border states and territories like Kentucky or New Mexico.
But yeah, they would've certainly been highly tied to Britain and France because of their cash crops.
Edit: Although they would've been pressured into giving up slavery like Peat said, if at the very least to raise their public image with the populations of their European trade partners/allies(?).