The Fly By Wire computer would maintain a speed above stall speed for whatever the configuration was and a fairly constant descent rate of maybe 800-1200 feet per minute - even hands off!
It wouldn't if both engines failed due to fuel starvation. Once AC power has been lost on both the AC transfer busses, the flight control mode reverts to secondary mode - envelope protection and autopilot is not available in this mode.
Once power has been restored to the busses, ie. APU start (the RAT only supplies power though the C1 and C2 TRUs to the captain and FO instruments and the L and R flight control PSAs), then the flight control mode may be MANUALLY reset, and the autopilot re-engaged. Obviously APU start is not an option with no fuel...