The resignations come after French luxury goods billionaire Bernard Arnault last week sold a 5.7% stake in Carrefour via Financiere Agache, his holding company.
Carrefour also said the company would appoint advertising group Publicis' chairman and chief executive officer Arthur Sadoun as a director and seek ratification at its next shareholders meeting.
(Reporting by Matthieu Protard and Sarah White; editing by Jason Neely)