First of all in cat III conditions you cannot Hand fly because your visual cues are insufficient for this purpose ! Remember in cat II or cat I a lateral element threshold light, approach light barrette or tdzl is required to provide "bank information" while looking outside ... In cat III conditions only the centerline lights are sufficient to confirm the correct position of the aircraft ! So it's a question of visual cues and not a condition of aircraft or rwy capability ! You always plan for the higher category supported by your A/c and your rwy because you dont want to waste an approach just to change your minima and your briefing if the conditions have change (you start with 300 rvr and you setup your catiiib a /c for a cat II only app ... Then at 900 your rvr falls to 200
)
According to airbus : if no flare at 30ft
If visual reference are sufficient
Disengage the autopilot and complete manually the landing
Nevertheless some operators SOPs order a go around in case of "no flare"
BUT ! If you have an emergency for ex a fire on board use your airmanship during your briefing to decide about your action in case of no flare....