PARIS—The European Union’s top court is set to decide whether the bloc’s “right to be forgotten” policy stretches beyond Europe’s borders, a test of how far national laws can—or should—stretch when regulating cyberspace.

The case stems from France, where the highest administrative court on Wednesday asked the EU’s Court of Justice to weigh in on a dispute between Alphabet Inc.’s Google and France’s privacy regulator over how broadly to apply the right, which allows EU residents to ask search engines to remove some links from searches for their own names.

At issue: Can France force Google to apply it not just to searches in Europe, but anywhere in the world?

The case will set a precedent for how far EU regulators can go in enforcing the bloc’s strict new privacy law. It will also help define Europe’s position on clashes between governments over how to regulate everything that happens on the internet—from political debate to online commerce.

France’s regulator says enforcement of some fundamental rights—like personal privacy—is too easily circumvented on the borderless internet, and so must be implemented everywhere. Google argues that allowing any one country to apply its rules globally risks upsetting international law and, when it comes to content, creates a global censorship race among autocrats.