So the Ottoman Empire was considered European? And the bit where I did qualify my statement with "German and Italian unification saw a few minor conflicts and there were a few civil wars"? Which leaves us with:

1823 French invasion of Spain (although this was part of a civil war)
1885 Serbo-Bulgarian War
1897 Greco–Turkish War

Which (even if you include the one's you omitted) comfortably fall into a "few minor conflicts". Indeed, the list of conflicts you give is about the same length as it has been since the founding of the treaty of Rome - so while the EU has helped the cause of European peace, I would not get too smug about it either and presume that this is why we've had such a long period of relative peace.

If you disagree with me, I suggest you google the European State System and perhaps the foreign policies of Bismark too or look at the various conflicts we've seen in the last sixty years.