GDPR and domestic French legislation applies to data held by the state (with some exceptions)
Most French government sites seem to place the information consistently at the bottom of the page under Personal Data and Cookies (Données personnelles et cookies). For the Ministry of Education:
Vous pouvez accéder aux données vous concernant et exercer vos droits
d'accès, de rectification, de limitation, d'opposition que vous tenez
des articles 15, 16, 18 et 21 du RGPD, par courriel auprès de la
délégation à la communication via le formulaire "À propos du site".
You can access the data concerning you and exercise your rights of
access, rectification, limitation, opposition that you hold articles
15, 16, 18 and 21 of the RGPD, by email with the delegation to the
communication via the "About the site" form.