If you look back to the Renaissance - one of the greatest ages the world has ever seen – we cannot attribute its impact on the world to a single date, or person, or breakthrough. Or the enlightenment - we cannot say with certainty when or by whom or how it was launched, merely that today’s Europe and today’s world couldn’t exist without it.
The Renaissance & Enlightenment are indeed integral to modern Europe's identity. The environment in which they occurred is the opposite of what the European Parliament stands for though. One of the most striking things about the lives of Renaissance and Enlightenment figures is how many of them had to flee their home countries and live part of their lives in exile.
This was only possible because of the political fragmentation of Europe, so people who might be persecuted in France could escape to the Dutch Republic or Venice, someone being persecuted in one German state could move to another. If there had been a 18th Century EU, with a European arrest warrant, the intellectual freedom of that era could not have existed.
The common characteristics of European civilisation only developed because there was no common European power. Concentration of power is a bad thing, even if some good comes out of it in the short term in the long run stagnation will set in. The examples of the Roman Empire and China serve to demonstrate this.
The Romans allowed their better Emperors to centralise a great deal of power, but the same powers that were exercised by Augustus or Marcus Aurelius could just as easily be used by a Nero or a Caligula. The same is true in Europe today- I can think of several positive things that the EU has accomplished, the promotion of free trade, encouraging Eastern Europe to reform, helping to face down Russia's attempt to rig the Ukrainian elections a few years ago and probably various other things- however the same centralisation of powers could just as easily be employed in the service of protectionism, isolationism & appeasement if political fashions change.
Therefore it is important that the European Union does not gain any more powers that lead to it being a European government and much of it's current powers to legislate on matters that should not be transnational (like working hours) should be revoked. Which is why scepticism is the right way to approach the EU.