@Francis,
I believe, however, that your parents, even if dead, inherited their French nationality your grandparents, and can bequeath it on you. I admit, though, that this is second-hand information. I have a friend whose French teacher acquired a French passport although neither of her parents ever had one. This worked because three of her grandparents were French when they immigrated, and noone along the chain had ever renounced their French citizenship.