This answer notes that participant nations have jurisdiction over their modules. So in a US module, you are in US jurisdiction, etc.
Which means that in an European module, you are in European jurisdiction. But Europe isn't a nation with one jurisdiction, but an union of sovereign states with their own jurisdiction and bound by treaties. Even more confusing, the ESA and the EU are not the same, some nations are part of one but not the other.
In a comment, the author adds from a linked resource that: "The European States are being treated as one homogenous entity, called the European Partner on the Space Station. But any of the European States may extend their respective national laws and regulations to the European elements, equipment and personnel." Which is, as the author says, "almost more confusing".
So how the hell does that work? To use the same example of this question, what would happen to someone being born in an European module? What if a crime was committed? What if someone took residence there? (Those are mostly hypothetical examples, to illustrate how jurisdiction works in this case.)