Formal:
* Adieu, mon amour. (This is the most classic and formal way to say farewell.)
* Au revoir, mon amour. (This is also a formal way to say goodbye, but slightly less formal than "adieu".)
Informal:
* Ciao, mon amour. (This is a casual way to say goodbye.)
* Bisous, mon amour. (This literally means "kisses" and is a very affectionate way to say goodbye.)
* Je t'aime, mon amour. À bientôt. (This means "I love you, my love. See you soon.")
Romantic/Poignant:
* Je t'aimerai toujours, mon amour. (This means "I will always love you, my love." It is a very romantic and heartfelt way to say goodbye.)
* Je me souviendrai toujours de toi, mon amour. (This means "I will always remember you, my love." It is a sentimental and emotional way to say goodbye.)
The best way to choose which phrase to use depends on your relationship with the person and the situation.