After discussion with an HR specialist:-
Here's the link
which should answer all your queries.
Contractually (and probably legally) it would appear that you would have to give 6 months notice prior to leaving. French companies usually state such a notice in their offer letter so that they can have sufficient time to source a new candidate.
If you wanted to leave, say after 3 months (for example having accepted another employment) you would have to state personal grounds for leaving. Or, if you are on good terms with your manager, try to renegotiate the initial 6 months down to 3 months.
Q- What would happen if you left early without having the agreement of the company?
A- You would lose all benefits and other compensation during the 6-month notice period (which is normal and which is most common, employees leave a company to join another so they should not be able to benefit from the former company's compensation/benefits plan).
- The company could request that you pay X amount to compensate those 6-months 'not worked' or other fees - this could get ugly - and a visit to the office of the Ombudsman could be in order to seek for advice, and see what is the common practice of companies in that region.