Europe culturally has, and will always will be highly separate. Let's go farther than countries, even smaller ethnic groups don't get along. Maybe what pops into mind are the Serbs and the Bosniaks, stuff in the Balkans, etc., but even as far West as Belgium groups such as the Flemings and Walloons have been at each other's throats since the birth of the nation state. The European Union is a good idea as far as a loose confederation goes, but in my opinion, it could never become a true nation state, and would be wrong to make it one by crushing Europe's beautiful and diverse cultures.
Although the European Union has had a lot of successes, there remain large differences in the political cultures of the different members. These different standards are one reason for the current economic crisis in Europe. Unfortunately, the nations will never be able to agree on important issues because of these differences.
Until very recently one would go to France and not assume that it had a lot in common with, let's say, Greece. You could enjoy each country for its own culture and food and ideology. Now there is supposed to be a shared culture with the European Union, but it has been artificially created.
By its very nature, the European Union lacks a shared European political culture. Each country features its own dominating political values and whatnot. With that in mind, the EU needs to work on creating a more unified political environment to avoid infighting and other problems. Otherwise, the EU will be in a weakened state.
Of course there will be infighting and compromises that need to be made, but there is certain amount of collective political identity that much of the European Union shares. The European Union does have some policies such as heath care, military policies, etc that most of the EU share which help create a common political culture.
No, the European Union does not lack a shared European political culture, because there are many things that Europeans have in common. Ethnically, Europe is diverse. Politically, however, they are quite unified, and generally agree on what combination of democracy and socialism they want to be in place in their societies and in their union. Because they agree on this, they work well as a unit in the European Union.