From what I have gathered so far is, the A320 does not have the reactive windshear warning generated via the EGPWS (mode 7), but via the FAC. On the B737 Windshear warning is generated by the EGPWS, it not optional.
This mentioned in the Mark V and Mark VII EGPWS Pilot's Guide shared by Captain Mongo.EGPWS windshear is provided for certain (not all) aircraft.