Latest revision to QRH - TR 608-1.
The flight director is not required for CAT II and CAT III landing operations.
The loss of landing capabilities is related to the loss of the AP, and not to the loss of the FD.
AS a result, the FD information was removed from the first line of the required equipment list that takes into account the AP.
VALIDITY:
All A320 family aircraft
So no, you don't need FDs. Hope that answers your question.