No, it is not possible to terminate your contract early. However, the French Labour Code provides for certain types of early termination:
On the employer’s initiative : If this is the case, the employer must propose a new employment contract taking effect within a maximum of 3 days of the termination. The new contract must comply with the same conditions as the previous one.
On the employee’s initiative:
during the trial period
if hired on a permanent contract
in the event of force majeure