Fadec fault means both fadec channels are at fault which will result in engine falmeout....
Fadec system fault triggers when "no dispatch" failure affects the engine (failure of sensor, channel, etc....) And does not lead to the loss of the engine....
Further, you could get "eng Fadec fault" on ECAM but the engine is still running and this is because the fadec is still powered but the connection between fadec and EIS (ecam) is lost....in this case check to see whether the engine is still running by checking other sys pages (elec, bleed....)