@sguzik,
Well, you could apply for French nationality.
French laws stipulate that is French a person that one parent at least is French.
I assume your mother didn't renounce to the French nationality (gave up by declaration), so she is still French.
The fact that her passport and ID card expired has no effect on her nationality.
After some procedures, you could get the French nationality and, by the very same article cited above, your own child would become French.