There would have been increased influence on the continent, a market to trade slaves particularly because the English had banned the Practice. Was it a failure of diplomacy, a sense among established countries that the odds were stacked against the South?
Slavery. The world was phasing it out. European countries in general had abolished it and had no need for it. Supporting the South was supporting slavery and the cost of doing so was not worth any small benefit they would derive. Most the European countries were just incapable of supporting the South across the Atlantic in the face of the U.S. navy if they had wanted to.
The British were the world leaders in abolishing the slave trade. As long as the South supported slavery, and was specifically fighting to maintain the institution Britain was not going to support them.
France had other interests, mostly Mexico. They were the closest to doing something in favor of the South but pressured by GB to stay out of it.
Spain was a geriatric country which hadn't been able to maintain its own empire much less assist someone else.
Germany and Italy were not united and the small states making them up had no real naval presences to make the attempt to help the South if they had wanted to.
Russia was allied with the U.S. (the Russian fleet spent much of the Civil War in New York harbor) and in disputes with Great Britain. Supporting the South would be tantamount to giving in to GB as Russia needed the potential alliance with the U.S. navy not some backwater agricultural nation.
The Austrian Empire was traditionally a land power with a small fleet. it was more concerned about neighboring Russia and the Ottomans and its own internal nationalist problems than some country half the world and an ocean away.
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