So yes, it was a civil war.
Remember that the Confederacy was never recognized by the U.S. as a separate country. They couldn't even get recognition from non-belligerents. For example, Jefferson Davis sent envoys over to Europe but they were snubbed because even Britain and France could see that their claims that they were their own nation were preposterous.
Diplomatic relations are only given to nations. Europe viewed this as a civil war, not a war of the Southern Nation against the Northern Nation.