although i am not of course the eu itself, nor do i even live there, i think this is incorrect
world war i lasted from 01914 to 01918 and killed 17 million people
world war ii in europe started 21 years later, lasting from 01939 to 01945 (though it started earlier in china) and killed 73 million people, mostly in russia
the 'european communities' were founded in 01952, 7 years later, and later grew into the eu. their single most important project was, and is, preventing or at least delaying world war iii, because it was, and is, widely believed that world war iii will kill a substantial fraction of the world's population, reducing the level of human development substantially and possibly causing human extinction
this is commonly believed to be more important than the single market, even, i venture to say, within the eu
world war iii may have started now; in retrospect, we may decide that it started in february 02014
the post is of course correct that the single market was a major instrument of this peace from the beginning, but it was and is only one such instrument, not the final product. in terms of keeping governments from bombing each other, probably the atomic cooperation is even more important