I was born in France of French parents who moved to the US and became US citizens. I lived in France until the age of 10. I now live in the US but would like to hold a French passport as well. I do have a birth certificate and French passports from my grandparents, and of course am fluent in French but I don't know how to proceed further.
The procedure is detailed on service-public.fr (check the “À l'étranger” tab). The only somewhat problematic item is:
Acte de naissance (copie intégrale ou extrait avec filiation) de moins de 3 mois : original (sauf en cas de naissance à l'étranger ou dans une ville dont l'état civil est dématérialisé ) + Justificatif de nationalité française si l'acte de naissance ne suffit pas à prouver la nationalité : original + photocopie
In your case, your birth certificate should be enough to prove your French citizenship. Specifically, it is definitely enough if at least one of your parents was also born in France. If not, you are still a French citizen (because at least one of your parents was French at the time of your birth) but you need to prove that (I can detail how if that's your case).
Note that if your purpose is having some document suggesting you are French, voting, or using your French citizenship anywhere in the EU, a national ID card is enough and much cheaper (free if you never had one, otherwise there is a €25 if you cannot present the previous one). And if you want to have definite proof that you are a French citizen (e.g. to make it easier for your children born abroad to prove they are French citizens themselves), then a certificat de nationalité française is the best document to have.
Since you will need a US passport to reenter the US anyway, a French passport is only ever required to travel to a third country and avoid a reciprocity fee, go to a place where French citizens don't need a visa but US citizens do (Venezuela being the only one I can think of at the moment) or perhaps if you want to avoid revealing that you are US citizen or hide some entry stamps present in either passports.