I have dual American-French Citizenship but speak limited French. I would perhaps try living in France some day.?

Perhaps you will, but you'll probably want to brush up on your French a bit before trying it.

You are a citizen and can apply for citizen services. You would have to register with the agencies that provide the services you seek. This is quite different from a non-citizen resident. Both would have to apply (register) of course, but you wouldn't even be allowed into the country as a resident without meeting all the resident requirements (a job being a pretty important one).

You don't migrate until you have a job and place to live both of which you can get before you move, the internet is a wonderful invention and companies advertise online as you would not qualify for benefits regardless of being French as you have not contributed nor lived in France for the required time to qualify

There are immersion programs both in France and in the USA that can help you achieve proficiency, which is the minimum practical requirement for you to work in France.

Regarding details such as enrolling in the French equivalent of social security you can visit the French Consulate nearest to you.

You may be able to work for a USA company or organization in France since employing you would be easier due to you not needing a work visa. Same with working in other EU countries. My dual-national friends who don't fluently speak the language of their EU country nationality use their European passport to work in another EU country where they do speak the language.

France and the USA have an agreement regarding social security:

https://www.ssa.gov/international/Agreement_Pamphl...

Work on your French.

You can get by on the basics, but not good enough for getting a job, communicating properly, and integrating.

Go for it.