I just joined so I hope you already found your answer. You have the right to French citizenship, in fact it is automatic.
I quote SOS-Net Etrangers:
Si vous avez au moins un parent français :
Vous êtes automatiquement français, que vous soyez né en France ou à l’étranger.
I translate:
If you have at least one French parent, you are are automatically French, whether you are born in France or abroad.
Source:
Droit des étrangers : SOS-Net Étrangers en France.
Its just paperwork now. If you haven't already done so you could start here: consulat général - Service de l'état à New York : (212) 606-3651 ou (212) 606-3637.
But your question asked about dual citizenship. Now that you know that you are French, the question is are you allowed to keep your American citizenship once you get your French papers? The answer is yes, but I don't have a written source.
I had read somewhere a subtlety about this but no longer have the source. The subtely was: If a country gives you citzenship without your having asked for it
--this is your case since yours is granted automatically--
then the US has nothing to say. However, if one asks for citizenship of another country
--this is my case--
the US may remove your US citizenship. However this appears not to be so...
I asked someone at the US embassy here in Paris if I (who am not French but married to a French man) could ask for French citizenship and keep my American citizenship and he said yes, the US cannot take my US citizenship away for having obtained French citizenship.
I do have a source for this next item :
You can even vote in France (if you lived here) without losing your Amercian citizenship, since 1978.
I quote:
En 1967, une décision de la Cour Suprême des Etats-Unis, suivie en 1978 par un vote du Congrès, a fait en sorte que nul ne peut être déchu de sa nationalité américaine pour avoir pris part aux éléctions de son autre patrie, s'il n'a lui même, auparavant, déclaré vouloir y renoncer.
I translate:
In 1967, a decision by the US Supreme court, followed by a congressional vote in 1978, declared that no-one could have their US citizenship removed for having voted in an election in his other country, unless he had at some time expressly declared the wish to renounce his US citizenship.
Source:
http://www.france-amerique.com/guide...itdevoir7.html
-an American in Paris