POLITICS in the EU
Europe is a continent made up mostly of liberal western democracies. Most of these democracies are based on the parliamentary system, which is based upon a parliament composed of elected representatives of the people. The parliament will then choose a government, the European parliament, which is elected by the population of the member states. The parliament then nominates a president of the EU in much the same way, but the president is elected by the European heads of state, this is an area where Denmark and the EU are nearly the same, but there are differences.
One of these differences is the amount of citizen participation in the systems. In Denmark the parliament must discuss any proposal with 50.000 signatures, this ensures that any legislation can be brought up by the people and with the internet this has become even easier. It is quite a bit harder to petition for legislation in the EU as you need 2.000.000 signatures, therefore the EU can often seem very distant to many citizens of Europe as their ability to influence the agenda is extremely limited. It would in many respects be admirable and advantageous for the EU to establish a channel of communication between the parliament and the people, as many EU citizens agree that the EU often can seem very distant and opaque.
Brussels is also known for having an enormous lobbying industry, one far larger than the one surrounding the Danish government. Lobbying generally diminishes the influence of poorer citizens in favor of others who are more well off, and can therefore be seen as antidemocratic. This is also something that many Europeans find repulsive as the mixing of capitalism and politics is looked down upon far more than in the United States.
Europe is built up of multiple treaties, starting with the Coal and Steel Union. These treaties compose the backbone of the European Union, and provide the basis for the system of government. Therefore there is no real need for the EU to have a constitution, as the EU already has a de facto constitution built up of these treaties. But if the EU did have a constitution it would make them able to act closer to a nation state and thus be less dependent on the US both in terms of trade and security, which might overlap with the popularity of security independence with European heads of state at the moment.
In 2004 a treaty established a draft Constitution for Europe, it was drafted in June 2004 and was later signed in October of 2004 in Rome, Italy. The draft was prepared by the Convention on the future of Europe. People like the EP President, Josep Borrell Fontelles were in attendance to sign the draft constitution. The reason for the failure of the European draft Constitutions was that not all the members of the European Union signed the draft. It was rejected by France and many other EU countries, only 13 EU countries signed the Treaty and back then there were 25 member states in the EU.
In conclusion the European Union's democratic systems are very similar to that of Denmark, but they are less transparent and allow for less participation. We can also conclude that a constitution would be a step in transforming the EU into a closer union and therefore allowing for more strategic independence.
Sources:
https://op.europa.eu/webpub/com/eu-what-it-is/da/
http://www.hrcr.org/hottopics/EuropeanC.html
https://european-union.europa.eu/principles-countries-history/country-profiles/denmark_en
https://newleftreview.org/issues/ii11/articles/jurgen-habermas-why-europe-needs-a-constitution