As posted above the Airbus has a very basic FBW system. Spins have so many modes and types that it can be very difficult to identify if the aircraft is spinning and what mode. Even more advanced FBW systems incorporating rate motion feedback can't recover from a spin. In fact the most important step in spin recovery for the F18A was to disconnect the FBW computers and go to direct electrical link. The Airbus does not allow pilot selection of that option.
You would also have to do extensive spin testing on the aircraft in order to determine the proper recovery inputs for each spin mode and CG situation.