This is a tricky one because US and French law have different rules when it comes to legal privilege. In the legal context, "privileged" means that the document normally cannot be used as evidence in a lawsuit. I say "normally" because there are exceptions and the privilege can be lost or waived.

The classic example of privilege is attorney-client privilege (see link: https://en.wikipedia.org/wiki/Attorney–client_privilege), but there are other privileges too. Every country that recognizes privilege at all has its own rules on what types of privilege exist, how privilege is established, and what exceptions there may be.

I've seen French texts using the term "secret professionnel" for documents that were protected because they were communications with attorneys or were created by attorneys. So this translation works, but hopefully the reader understands that the term doesn't mean EXACTLY the same thing in French as in English, because the rules on privilege are different in each jurisdiction.