None of these things are required to be a French citizen (and conversely, being a French citizen is not required to get a carte vitale or social security number) or even, technically, to live in France.
If you come to France as an adult, you can get a carte vitale from the CPAM when you first register for health insurance:
- If you work, you will be insured through your work.
- If you are a student at a higher education institution, you will have to register with one of the approved students' health insurers (usually you do that together with all other registration formalities). Not sure about students at secondary schools, the assumption is that they are usually insured through their family but there must be some procedure for those who aren't.
- If you live with your parents or a spouse/partner, you can also be covered by their insurance, at no extra cost.
- If you have no other way to be covered, you should contact the local CPAM directly to get the Couverture Maladie Universelle.
You will also automatically get a social security number when you get (statutory) health insurance for the first time. You don't really need to do anything now to be a citizen or reside in France legally and could therefore wait to find a job (if that's what you want to do) and sort it all out afterwards.
But of course having health insurance as soon as possible would seem a good idea and you could therefore simply apply for the CMU immediately. The costs of the insurance premium will depend on your income for the previous year (you will need tax returns from the country where you resided previously) and it's free if you had no income.
An ID card, while useful for many purposes and nearly universal, is not legally required for any purpose. In particular, your passport should do just fine when interacting with the authorities and if you need to prove your citizenship, the certificat de nationalité française, and not the carte nationale d'identité, is the strongest form of evidence.
A tip: Whatever you do, you will need a copy or extract of your birth certificate for many things, you can already prepare those.