My mother was born in France, married my American father had 5 children, became a U.S. citizen then had another child. Are we eligible for dual citizenship between France and the U.S.

Most European countries will grant dual citizenship. Apply at French consulate. Also, I'm sure you could call them to get more info.

If your mother was a French citizen at the time of your birth, then you are also French. The consulate can help you.