If you are employed by a foreign company subject to the French social security system, you must be registered with the primary healthcare fund (‘Caisse Primaire d’Assurance Maladie’ - CPAM).
If you are a citizen of a non European Union member country, you must hold a residence permit (‘titre de séjour’) or a work permit (‘autorisation de travail’).
All information on Work permit for a foreign employee in France | Service-public.fr.
You may contact the CPAM of the place where you live for information about joining the scheme and obtaining your health insurance card (‘carte Vitale’).
If you are off work sick, you must sent sections 1 and 2 of the corresponding certificate to your CPAM and section 3 to your employer. Further information can be obtained on-line by logging on to the ‘Ameli’ health insurance site.