Formal:
* Je suis le/la directeur/trice. (This is the most literal translation and is suitable for formal settings.)
Informal:
* Je dirige. (This translates to "I direct," and is a more casual way of saying you're the director.)
* C'est moi le/la directeur/trice. (This is a more emphatic way of saying you are the director, and is often used in informal settings.)
Context-specific:
* Je suis responsable de la direction. (This translates to "I am responsible for the direction," and emphasizes your role as a leader.)
* Je dirige l'équipe. (This translates to "I lead the team," and specifies your role within the organization.)
The best way to say "I am the director" in French will depend on the situation and the level of formality required.