Even a national privacy authority, and not just the Irish one, can sue Facebook in case of violation of the data protection directive (GDPR): this was established by the Court of Justice of the EU, in a ruling that sees the 'Belgian data protection authority against Facebook Ireland, Facebook Belgium and Facebook Inc for collecting data through cookies, in violation of the directive.
The Court clarified that, although the Irish authority is the "lead" of the data processing given that Facebook Ireland is the data controller, the other national authorities can also act in court.