Constitutions don't enforce themselves. The US constitution has a crystal clear right to bear arms but multiple jurisdictions ignore it and multiple supreme court rulings and make firearm ownership functionally impossible anyway. Free speech regulations have, thankfully, been more robust.
The only thing that stops bad things happening is a critical mass of people who believe in the values the constitution memorializes and who have enough veto power to stop attempts to erode these values.
The US has such a critical mass, the gun debate notwithstanding. Does the EU have enough people who still believe in freedom?