take proof i.e.mother's birth cert and her passport, you just cant ask for a French passport you will have to take her nationality [ I think] first and this takes approx 6months, well it did for someone I know who changed his nationality to Portugese] also are you asking for dual nationality or are you willing to give up your English one if necessary ?
If you already have an English passport, now we are in the Common Market what benefits will you get from having a French Passport also ?
good luck, but it will be time consuming and be prepared for long waits at Embassies + costs.Whatever you do dont involve lawyers that will really cost.