I'm not entirely sure that I follow this argument- there has always been a rich, vibrant and common European culture regardless of political divisions. However people who oppose the political unity of Europe are against a common European culture.
The periods of innovation and cultural exchange within Europe came during an era where political repression was common but political disunity allowed those being persecuted in one juristiction to seek sanctuary in other places. So to use that common history as an argument for a political union (complete with a pan-European arrest warrant) is not much of an argument.
A delectable sense of freedom
29 minutes ago