Formal:
* Je suis désolé, mon amour. (This is the most common and literal translation.)
Informal:
* Je suis désolé, ma chérie. (This is a more intimate and affectionate way to say it, using the familiar "chérie".)
* Pardon, mon amour. (This is a more casual and everyday way to say "sorry.")
* Je suis désolé, mon cœur. (This is a very romantic way to say "I'm sorry".)
Note: You can also use a more specific phrase to apologize, such as "Je suis désolé de t'avoir fait attendre" (I'm sorry for making you wait) or "Je suis désolé de t'avoir blessé" (I'm sorry for hurting you).
Ultimately, the best way to say "I'm sorry, my love" in French is the way that feels most natural and sincere to you.