Not all states have monolithic cultures or one homogenous culture. Canada, for instance, is a multi-cultural and multi-lingual federation. The Quebecois are a distinct cultural group of French-speakers within that nation.
The UK is another characteristic example. It is a nation comprised of between 4 and 5 countries (5 if you include the Cornish) with distinct cultures, languages and even legal systems: Scotland, England, Wales, Northern Ireland and Cornwall. I studied and became qualified in Scots law. To practise as an English lawyer, I need to do a conversion course and another traineeship, just to relocate my practice to somewhere else in my own state because Scotland and England have different systems. Scots Law has different sources from English law.
Scotland has a proud and distinct culture from England. We are not the same, yet we have full political unity as regions within the UK.
In terms of Europe, there certainly is a shared heritage anchored in medieval Christendom, the Renaissance, the Enlightenment, the Holy Roman Empire, the Scientific Revolution
et al. Nazism, Communism and the Iron Curtain were also shared experiences.
And there is a powerful foundation narrative for the EU as coming out of the carnage and bloodletting of WWII.
Read:
euperspectives.blogactiv.eu/2014/06/13/a-reflection-on-european-unity-the-eu-and-the-memory-of-christendom/
“Europe” is not an empty term. Before the nation-states of modern Europe existed, Medieval Christendom existed.
The unity preceded the divisions.