Informally these could go (where I'm from anyway):
- Comment ça va?
- Moi c'est ___.
- Heureux de faire ta connaissance.
It's the same thing but using "tu", and shorter and "less correct" words.
I am sure certain domains or settings have more formal rules, but in general, French does not have a very codified way of presenting oneself that I can think of.
One thing that is important in a formal setting is to use "vous" to address people directly. It's the polite (or plural) version of you.
A common formal introduction would consist of:
- a greeting ("Bonjour" works as long as the sun is not setting or it's not dark outside)
- optionally asking the other person how they are doing ("Comment allez-vous?")
- telling your full name ("Je m'appelle ___.")
- telling the other person you are glad to meet them ("Enchanté de faire votre connaissance.")
Of course, the other person will respond and ask you similar questions in between those.