In France, everyone has access to a basic public health insurance system. It is funded through taxes, and all residents can benefit from it. Each French resident can obtain a Carte Vitale, which is used to access healthcare services—for example, to pay for a doctor’s visit.

To get the actual card, you need to follow these step :
https://www.service-public.fr/particuliers/vosdroits/F265?lang=en

You should need :
 Copy of your passport
 Copy of your titre de séjour or récépissé
 Copy of your birth certificate
 Copy of verified translation of your birth certificate
 Copy of job contract
 If you are married/have children also copies of those docs
 IBAN from a french bank (official document that you can download from your bank account)
 Proof of residence (electricity bill or rent contract)

Then take those documents and send them by post to the following address :
Assurance Maladie
SRI/Talents
75948 PARIS Cedex 19
(to be confirmed — can it be done only ????)

After 2-3 months you will get a reply where they will explain how to get a Carte Vitale – medical insurance card. Basically this type of insurance is managed by CPAM at which website you will have the account once social security number is assigned to you. In principle, people from University can transfer their social security to be managed by MGEN, but for basic insurance it should not make any difference.
This is only for basic insurance, which covers only around 80% of expenses, depending on the type of treatment. The additional insurance is called mutuelle and provided by many companies, including MGEN (just google it) and covers different things with the rate up to 100% but for this you have to pay extra 20-60 EUR per month depending on coverage type.