No. The EU isn't a federation, there's no supremacy class. The member countries are sovereign and obviously can't go against their constitutions or basic laws.
> The member countries are sovereign and obviously can't go against their constitutions or basic laws
False.
> The principle was derived from an interpretation of the European Court of Justice, which ruled that European law has priority over any contravening national law, including the constitution of a member state itself.
That is sort of like a supremacy clause, and of course it's valid for the EU.
But that doesn't mean that a Swedish or German etc. court can let that override our basic law. Our basic law is after all the foundation of our law, so if something conflicts with that, it obviously can't be valid.