OK, I admit to being (more than) a bit overzealous on that point. Still, peace has existed within the borders of the EU and its predecessors since the formation of the ECSC (one of the EU’s predecessors) in 1951.
Even if you disregard that point, though, the overarching point of my comment still stands.
After WWII Europe was occupied by the allies on one side and the Soviet Union on the other side. It was called the cold war and peace was guaranteed by mutually assured nuclear destruction. Not by the European Union.