All European countries have similar authorities (such as the ICO in the UK, for instance). Together, they make up the G29, a larger organisation whose aim is to standardise European data protection rules.
CNIL (Commission Nationale de l’Informatique et des Libertés)
The CNIL is an independent French administrative authority whose mission is to ensure that information technology does not infringe on human rights, privacy or individual and civil liberties. It determines the terms and conditions for data collection and use.