General sense of leaving one's home:
* A quitté son domicile: This literally translates to "left his/her home."
* A déménagé: This means "moved out" and implies a permanent departure.
Leaving home for a specific reason:
* A quitté la maison pour...: This means "left the house to..." and is followed by the reason, for example:
* ... aller au travail: to go to work
* ... partir en vacances: to go on vacation
* ... voir un ami: to see a friend
* ... faire des courses: to go shopping
Leaving home permanently:
* A quitté le nid familial: This is a more figurative way to say "left the family nest" and implies leaving home for good.
* A quitté le domicile de ses parents: This translates to "left the home of his/her parents."
Examples:
* "J'ai quitté mon domicile pour aller au travail." (I left my home to go to work.)
* "Elle a déménagé chez sa sœur." (She moved out to her sister's place.)
* "Il a quitté le nid familial à l'âge de 18 ans." (He left the family nest at the age of 18.)
The best way to say "left home" in French depends on the specific situation and the level of formality desired.