Google is fighting a big battle in the European Union's top court about whether people's "right to be forgotten" should apply globally to its search engine.

Private citizens in Europe can ask Google and other search engines to remove certain unflattering results about them.

France's data-protection agency said that Google deleted results only from its EU search engines and that the information remained visible on non-EU domains.

Google argued Tuesday that applying the rule globally would impinge on people's right to free expression.

Most people outside Europe don't know much about the digital "right to be forgotten," the idea that private citizens can ask search engines to scrub certain results about them.

It's a comparatively new idea, but a landmark ruling in 2014 from the European Court of Justice set the initial parameters of how it might apply. That ruling said search engines like Google could be forced to delete results.

That ruling is at the center of a thorny battle between Google and France's data-protection agency, CNIL, which is arguing that the right to be forgotten should apply to search-engine results globally, not just within the EU.

According to CNIL's complaint, Google does delete, or "delist," some results from private citizens when requested. But its main bone of contention is that Google isn't delisting the results everywhere. Some delisted information, CNIL said, was still visible on non-EU versions of Google.

On Tuesday, Google shot back at a hearing before 15 EU judges and said expanding the right to be forgotten globally would impinge on freedom of speech.

Bloomberg reported Tuesday that Google's counsel Patrice Spinosi described CNIL's proposals as "very much out on a limb" and in "utter variance" with other judgments.

Google isn't alone in arguing that deleting search results may equate to censorship. Media organizations including BuzzFeed, Reuters, The New York Times, and various nonprofits have argued the same.

"This case could see the right to be forgotten threatening global free speech," Thomas Hughes, the executive director of the freedom-of-expression group Article 19, said.

"European data regulators should not be allowed to decide what internet users around the world find when they use a search engine. The CJEU must limit the scope of the right to be forgotten in order to protect the right of internet users around the world to access information online."

You can read the case documents here.