There are no medical records on the chip
From
https://fr.wikipedia.org/wiki/Carte_Vitale (Google translate)
data recorded in the electronic component of the card:
the visible data mentioned above as well as the period of validity of the card, the surname of the holder if it differs from the name of use, his other first names if applicable, his date of birth, his address and the photograph digitized identical to that appearing on the card,
data relating to rights to benefits in kind under a basic health insurance scheme,
the data relating to the choice of the doctor treating the card holder,
the data relating, where applicable and subject to his consent, to the holder's situation with regard to the complementary health insurance protection,
the data relating to the situation of the holder in terms of accidents at work or occupational diseases and the last recognized accidents or occupational diseases,
data relating to access to care in the event of a stay or residence in another Member State of the European Union or part of the European Economic Area,
personal data concerning the contact details of a person to be notified in case of necessity if the cardholder has consented thereto,
the statement indicating that its holder is aware of the provisions of the regulations on organ donation,
data allowing:
ensure the implementation of electronic signature functions,
protect access to card information,
authenticate the card as a health insurance card and identify its holder.
You can read the chip using one of the reader terminals in the CPAM/social security offices and elsewhere. The chip contents are updated regularly.
The medical history you mention is Le Dossier Médical Partagé (DMP) They are going to have another attempt to get everyone to use it so an updated version is being launched this year see
www.dmp.fr