Firstly the West has been involved in Syria for centuries. Secondly every civil war, although starting as a local conflict, quickly draws in international players.
Actually the South's early strategic goals were built around bringing Europe into the conflict. The purpose of Lee's 1862 Maryland campaign was to demonstrate to Europe that the South could survive militarily and deserved recognition and support.
The CSA certainly tried to elicit the aid of France and Britain. The commerce raider the CSS Alabama was in fact built, outfitted, and crewed in Liverpool.