Formal:
* Quel est votre caractère ? (What is your character?)
* Quelles sont vos qualités ? (What are your qualities?)
* Que pouvez-vous me dire de vous ? (What can you tell me about yourself?)
Informal:
* C'est comment, toi ? (What are you like?)
* Comment es-tu ? (How are you?) - This is a more general greeting but can also be used to ask about someone's personality.
* Tu es comment ? (What are you like?)
More specific:
* Comment es-tu avec les autres ? (How are you with other people?)
* Quel genre de personne es-tu ? (What kind of person are you?)
It's important to choose the right phrase depending on the situation and your relationship with the person you are speaking to.