It might be a little too simplistic to credit the EU for 70 years of peace.
There is no major conflict directly involving two major powers for many decades (1945/WW2, or 1952/korean war if considering that China was a major power at that time, which is generous IMHO).
That's not limited to Europe, this statement is valid for the whole world.
Several factors can explain it:
* Better living conditions (far less frequent famines, less large scale epidemics, etc), mostly due to industrialization of many countries and consequently less tensions inside and between countries over resources.
* For a part, economic dependencies between countries.
* MAD, but also the realization after WW2 that a major conflict, using modern weapons, even only conventional ones, can only lead to both sides actually losing.
* Better worldwide coordination through the UN (imperfect, yet it helps).
* Better education for large parts of the world population.
* More pacifist views and reject of war.
This is still oversimplifying why there is this unprecedented peaceful period, but it shows the CECA/CEE/EU is far from being the only factor at play.