Not quite, the Western Union (predecessor to the EU by way of the was formed by the BeNeLux countries, the UK and France. Some of those were at war in preceding centuries but they were on the same side during WWI and WWII. It didn't have a lot of clout because very rapidly afterwards other more powerful institutions were formed and it was superceded. But it was more of a continuation of some of the collaboration that stemmed from being allies/liberators in the war than that they were on opposing sides. Later institutions included Germany and Italy as well.
As I recall, Churchill was a strong proponent of the EU's [edit: I can't believe I used the wrong word:] ancestor (the European Communities? Some oil and coal community?), as a way to prevent further wars. Churchill blamed nationalism specifically.
You're saying the EU wasn't required? That seems like a bold statement, but probably too much to sort out in HN comments.
I'm a bit confused by "but" in that sentence. I'm not sure if a 'not' or another word is missing there. Certainly many saw unification as beneficial - again, it was the key to many. Many still do.
Unification was underway prior to the EU, the EU is the eventual larger body but it took some steps to get to the point where it could be properly established, mostly on account of the various countries still reeling from WWII and being very busy with reconstruction efforts (and piss poor to boot, the first years after WWII were almost as bad as the last years of the war and in some places even worse besides the reduced immediate risk to life). Doubly so for those countries that ended up on the far side of the Iron Curtain, but then again, they weren't part of the EU for many years to come. But for many of them the only thing that changed is that German uniforms became Russian uniforms and usually that wasn't accompanied by a higher degree of civility by the occupiers.
How do you establish the arrow of causality (and of course, to some degree, it points both ways)? Objectively, we know that a major intent and design of the EU (and its earlier iterations) was to prevent another war.
The EU (in its early forms) was formed by the countries that just fought each other in WWI and WWII, and for centuries before that. The EU was specifically intended to prevent another war.