Je m'excuse.
This is a formal and polite way to apologize.
Here are some other ways to say "I apologize" in French, depending on the context:
* Excusez-moi. (Excuse me) - This is a more informal way to apologize, used for minor offenses.
* Pardon. (Pardon me) - This is another informal way to apologize, often used when interrupting someone.
* Je suis désolé(e). (I am sorry) - This is a more formal and heartfelt way to apologize.
* Je regrette. (I regret) - This is a more formal way to apologize, often used in professional situations.
* Veuillez m'excuser. (Please excuse me) - This is a more formal way to apologize, often used in written communication.
The best way to say "I apologize" in French depends on the situation and your relationship with the person you are apologizing to.