In OTL, the Confederacy tried to persuade the leaders of several northern Mexican states to join them. OTOH, an independant Confederacy would probably have to recognize the French puppet Maximillian in return for France recognizing them. And the various Confederate States were deeply divided over expansion.
There's a decent chance Maximillian will hang on until 1870-71, the Franco-Prussian War. Regardless of TTL outcome, France will be more worried about defending the homeland and Maximillian will probably fall from power shortly thereafter. OTOH, Jaurez dies in in 1872, so it's not a sure thing.
Still, you've got a good chance of a Mexican Civil War, perhaps even fragmentation. The CSA will probably attempt to seize northern Mexico, but this has a good chance of being divisive enought that the Confederacy splits over the issue. The USA might also attempt to seize Baja California and Sonora to stop CSA expansionism.