This sums it up: http://mshistorynow.mdah.state.ms.us/images/594.jpg
The UK and France were the large players, so let's mention them in more detail. Also worth mentioning at first, is that Europe had plenty of its own concerns during these times and colonial efforts were at a height amid the "Scramble for Africa", France's interventions in Mexico, gold rushes, industrial growth and railroad building, and other distractions.
The British effectively practiced neutrality. This was the Victorian era and the Empire's 'Golden Years', their industrial revolution in full swing and colonialism abound. The Trent Affair was one of the largest diplomatic incidences during the American Civil War and garnered a lot of press in Britain and across Europe...probably the closest they came to intervention. Britain as a whole was alarmed at the outset, when southern cotton and other goods no longer became available due to the Union Blockade. Textile industries took hits and many were indeed hoping for a quick Confederate victory or truce. Once Lincoln released the Emancipation Proclamation, Britain again had myriad concerns, specifically of slave uprising and race war, but public opinion was strong and the Union had the generally more favorable reputation. The US Civil War is often considered a catalyst for the sweeping Reform Act of 1867 which broadly increased workers and voting rights - where the Confederacy's model was seen to represent large upper-class landowners and the Union represented more democratic and popular social movements.
The French never recognized CSA legitimacy officially, and maintained neutrality - but the free presses in France varied their opinions on the civil war. The Confederacy was supported by Conservative factions, supporters of Napoleon III, Bourbon legitimists, and Roman Catholic interests. The Union had the broader support of republicans and Orléanists.
They supplied misc weapons and materials to both sides, often through intermediaries or with some difficulty (such as the CSS Stonewall ironclad ship that ended up being sold by France to Denmark Prussia, then ended up as Japan's first ironclad.
Further reading and cites:
The Times of London every newspaper in 1960s' http://www.thetimes.co.uk/tto/archive/
George M. Blackburn, "Paris Newspapers and the American Civil War," Illinois Historical Journal (1991) 84#3 pp 177-193.