British public opinion was divided on the American Civil War. The Confederacy tended to have support from the elites: the aristocracy and the gentry, which identified with the landed plantation owners, and Anglican clergy and some professionals who admired tradition, hierarchy and paternalism.
The people of France were not entirely in agreement. The Confederacy was endorsed by those who also supported Napoleon III and the Roman Catholics. French Republicans supported the Union.
From all I can see, aristocracy and monarchists in Europe tended to be pro-Confederate. In general, the kings of Europe were happy to see the US broken up and sympathetic to what they viewed as southern aristocracy.
It would have been difficult for anyone but Britain, France, or maybe Mexico to get involved. It was also seen as dangerous and not advantageous to get involved in a civil war.
Russia did sort of ally with the Union. Russia was worried about British and French intervention in the Polish rebellion. The US and Russia formed a common front to discourage intervention in either rebellion. Russia also did not want to see the US weakened, which might increase British power in the area. The Czar had freed the serfs and Russia had a very centralized system, so the US and Russia had some things in common ideologically.
Not sure why you think aristocracy favors centralization. Absolute monarchies, such as Russia, Spain, France, and China in the 18 century and before favored centralization. Aristocracy traditionally favored decentralization, as in feudalism.