If you were born to a French father, then you are most likely already a French citizen. You don't need to become one.
In practice, it depends on what you mean by “officially became his son”. If you have paperwork to prove both his citizenship at the time of your birth and the fact that he is legally your father to the satisfaction of the French authorities, then you should be able to get your French citizenship recognized. It's not up to the consulate to grant you citizenship or not, you “just” have to prove to them that you already have it. The fact that your father is presumably not mentioned on your birth certificate does make things a bit more complicated however. I am not sure exactly how you should go about proving all that in this case. Worse case, you will need to fight for it in front of the court system.
Incidentally, the two main avenues to actually become a French citizen without being born as one (namely “naturalisation” and “déclaration”) do not apply to you. You would need to either reside in France or be married to a French citizen. So you really need to get your French citizenship by descent recognized because nothing else would work in your situation.
Formally, since don't need to (and cannot) apply for citizenship, there is no specific procedure. But if you want to use that citizenship in practice (e.g. to vote or get a passport and travel to France), you will need to apply for an official document establishing it (ID card, passport). So you will need to make an appointment and talk to a consular officer but that's not a formal “interview” per se.
Since you presumably never had a French passport or ID card before, I think you will need to request a certificat de nationalité française and present that to the consulate to get your first national ID card. As you were not born in France, you will need to apply for the certificate by mail to the Service de la nationalité des Français nés et établis hors de France (see the website of the French consulate in Los Angeles for more detail).
If you are not comfortable reading legalese in French, you will definitely need someone who is to help you because most of the documentation is only available in French and the French authorities will expect you to address them in that language. Beyond that, the best is probably to hire a lawyer because it's not uncommon to have difficulties in getting the authorities to recognize your rights in this area. But it's not cheap and finding one that is familiar with nationality law from the US might not be easy.