If your parents didn't register your birth to the French civil register, you must petition for a French nationality certificate from the French Nationality Office in Paris if you reside outside of France (which I assume from the wording of your question).
Only then are you eligable to recieve a French ID/Passport and to be treated as an EU citizen.
A birth certificate issued in the US is not, in itsself, proof of French citizenship.
It can only assist in verifying French citizenship if at least one of the parents stated in the certificate are also French citizens.
Collecting the information about your parents (their french passport, ID, last address in France etc.) would be the first step.
Check if they actually registered you in the French civil register the second step (see point 2 of the french link below).
If not, start the application process with the Paris Court (service of French nationality), which I believe can be time consuming (see point 5 of the french link below)
You email or file your application (completed, dated, signed and supporting documents) Paris Court (service of French nationality).
2. Check your birth certificate
If you were born in Foreigner [outside of France]
If you do not have a recent identity document, proof of French nationality can be provided by presenting a birth certificate (full copy or extract with filiation) of less than 3 months.
This act of civil status can establish your French nationality if you are in one of the following cases:
- The birth certificate (on secure paper) was issued by the Nantes Central Registry Office.
- The birth certificate (on plain paper) was issued by an embassy consular vital statistics officer.
5. Request a certificate of French nationality
If you do not have any of the above documents, you will need to request a French nationality certificate (CNF).