Formal:
* Amusez-vous bien, mon ami/ma chère amie. (This is the most formal option, suitable for someone you don't know well or in a formal setting)
Informal:
* Profite bien, mon pote/ma pote. (This is a more casual way to say it, suitable for close friends)
* Passe une bonne journée/soirée, mon pote/ma pote. (This literally translates to "Have a good day/evening, my friend," and is a very common way to say "enjoy yourself" in French)
* Fais-toi plaisir, mon ami/ma chère amie. (This means "treat yourself," which can also convey the sentiment of "enjoy yourself")
Other options:
* Amuse-toi bien, mon ami/ma chère amie. (This is a slightly less formal version of the first option)
* Profite bien de ton temps, mon ami/ma chère amie. (This means "Enjoy your time, my friend" and is suitable for various situations)
The best option will depend on your relationship with the person you are talking to and the context of the conversation.