Very interesting question.
But we have to find out more about it.
Can you (or the FMGC) control thrust on an engine without FADEC? Looks like affirmative, since there are no INOP systems. This is very odd. So I think that in most cases this warning will be accompanied by an ENG FAIL caution.
These engines don't have any backup hidromechanic engine control. Without FADEC the engine will not work.
I think the procedure is to confirm if the engine has failed, thus confirming that the FADEC is indeed failed. IF CONFIRMED, after engine shut down procedure. If it is still working, the FADEC is not lost. Something else is going on. Don't shut down before finding out what's going on.
I'll take a look at the FCOMs to refresh my memory.