I'm not sure if any country supported either side officially. During the war, Both President Lincoln and President Davis wrote to the Pope. Davis got a response, and while the Papal States didn't officially recognize the Confederate States as a country, the letter was addressed to "the President of the Confederate States of America." Also, there's France under Napoleon III. In 1862 France landed troops in Mexico, drove President Benito Juarez out of Mexico City and installed Archduke Maximilian of Austria as Maximilian I, emperor of Mexico. The plan was to take control of Mexico and render aid to the Confederacy without really getting involved. Unfortunately for him, French and Mexican Conservative forces could not completely defeat Juarez and his liberals and plummeted Mexico into its own civil war.

Always more to be said, but do check out this FAQ section with several responses on European perspectives.