No, you cannot convert or directly change your expat health insurance policy into a mutuelle. These are two different types of insurance.
If you now have your French social security number (SSN), you can cancel your expat policy and sign up for a mutuelle.
The expat policy and the mutuelle are not connected, they serve different purposes.
A mutuelle is designed to work with the French public health system (Sécurité Sociale). The two are “linked” together via the télétransmission, which allows reimbursements to be processed automatically between your public coverage and your mutuelle.
The expat policy is not connected to the public system in this way.
The mutuelle also provides coverage for preventative care and routine check-ups, which are not typically included in an expat policy.
In short, Sécurité Sociale plus a mutuelle gives you the most comprehensive health insurance available in France. If you are eligible for the public system, it’s strongly recommended to switch to this combination.