The phrase "publicly owned" in English implies government-owned (which seems like the German.) I'm not sure that the phrase "public company" is a common one. "Publicly-traded"? Yes. A company "going public"? Yes. And people would know what you meant if you said "public company" in context, but they might think you were referring to a "public utility," which may or may not be government owned.

Also public and private schools (in the US.)