An early Confederate victory (or northern abandonment of the war, which wasn't unlikely) would have meant that cotton would have remained a powerful, mostly Southern resource. Only as the war dragged on did the British concentrate on growing cotton in Egypt and India.
Could the South have survived a victory? Given the amount of infighting and backbiting among the Southern politicians, one wonders. I can see three broad paths:
1) Confederate war hero has political clout to get slavery abolished, probably by gradual emancipation. Not likely.
2) Confederate 'pay-off' for recognition and support from France is recognition and support of Maximilian in Mexico. South concentrates on expansion in the Caribbean, Mexico and Central America. Attempts to export Southern plantation life to these areas probably fails.
3) Disagreement, disunion and collapse. If South Carolina would secede from the Confederacy during a war, she might secede during peace - and other states might go their own way too. The South becomes little more than an 'Americanized' banana republic.
Remember that, even without the Southern states, the Union created one of the largest armies and navies on the planet, expanded its industry and tax base, and was approaching Great Britain in literacy, population and key indicators of industrial output. Depending on the statistics you use, the US surpassed the European powers sometime around the turn of the century. So even if the North lost the war (or let the South go), there is no way it would have remained just a regional power.
For all that some people in the South wanted to industrialize, the fact is that they talked about it a lot but didn't act. Southerners by and large did not own or operate manufacturing plants, railroads, steamships or locomotives, make pig iron, rifles or cannon, endow schools, colleges or libraries. They did SOME of this, but on a tiny per-capita scale compared to the North, England or France.
There isn't any reason to assume that a victorious Confederacy - at least one that secured a relatively early victory - would industrialize. More likely they would go on as they had, expanding agricultural exports, keeping import duties low and buying what they needed in England.
I have to agree with Timothy Ortiz about the after-effects of Manassas (Bull Run). And add this - there was no political will for the South to invade and take Washington. Frankly they might have welcomed Maryland but not really wanted D.C. And they assumed that, having beaten the Northern invaders, the war would shortly be over. Look at the relatively large 'desertion' rates when Lee went into Maryland in the Antietam (Sharpsburg) campaign. Southern soldiers didn't understand why they should invade the North, they left in droves and came back after the army moved back into Virginia.