Dear Rana ,
If you want to know what are your rights according to the civil marriage made in France , specially concerning the costudy of the children you should review the french law . Because when there is a civil marriage the lebanese civil tribunal will apply the french law and give you in case of divorce your rights as a woman according to this law and not the lebanese one .
your husband can not marry another women , if he do so you can ask for divorce & you will get it , because there is no civil marriage that allows him to have more than one wife . But as muslim he can do it in Lebanon and marry another woman but as I told you if this happened the civil marriage protect you and you divorce him easily , but if you are married according to the Shariaa ( religious marriage ) than you can not divorce .

Hope that I answered your question .

Good luck