You have an automated manual transmission (Fiat call it "Dualogic"), not a traditional automatic transmission. This uses a conventional manual gearbox, with an electro-hydraulic unit on top that actuates the clutch and gear change.
The "gearbox fault" is probably a problem with this electro-hydraulic unit, possibly a failing hydraulic pump, or low hydraulic fluid level due to a leak. If it occurs again, get the car's diagnostic system read for the stored error code as this will help to diagnose the problem.