National Commission on Informatics and Liberty (CNIL) is the data protection authority in France. Their main objectives are to provide guidance and advice as well as deal with complaints and make inspections regarding data protection.
CNIL is renowned for its competence and body of work within IT security, Privacy Impact Assessments and cookie guidance.
Notable GDPR decisions: CNIL vs Google (transparency), CNIL vs Vectuary (data broker) etc.