The European Union has a reputation for being an institutional maze. It doesn’t help that its buildings often turn out to be actual labyrinths, stranding lawmakers, lobbyists and journalists on their way to meetings—and sometimes to their own offices. “I get lost all the time,” says Fabio De Masi, a member of the European Parliament representing Germany’s Left party.

A few weeks after he was elected in May, Mr. De Masi lost his way in the Parliament’s headquarters in Strasbourg, where delegates spend a week every month.

...