Yes, there is an internal battery.
What you described points out to the internal battery not having enough juice. If the battery was dead for such a long time, as you described it, the internal battery very much can loose its power.
And if the internal battery is not loaded enough, you loose all your in-camera settings, including date and time.
I would suggest to first put a fully loaded battery in your camera, and leave it at least overnight. That will load the internal battery.
Than you can adjust the settings in your camera.
BTW Fuji has a free app in which you can save (and reload) your camera settings. It is called Fujiflim X Acquire.
cheers,
Remko