Formal:
* Papa est parti. (Papa has left.) This is the most neutral and common way to say it.
* Papa s'en est allé. (Papa has gone away.) This emphasizes the fact that Papa is no longer present.
Informal:
* Papa est parti. (Papa has left.) This is also the most common way to say it in an informal setting.
* Papa est parti se promener. (Papa has gone for a walk.) This specifies where Papa has gone.
* Papa est parti chez sa mère. (Papa has gone to his mother's house.) This specifies the location of Papa's departure.
More specific:
* Papa est mort. (Papa has died.) This is the most direct way to say that Papa has passed away.
The best way to say "Papa has gone" in French will depend on the specific context and the message you want to convey.