A321 Captain reported a parking brake failure at the gate resulted in temporary uncommanded movement of the aircraft.

Narrative

We arrived at the gate in ZZZ; and as I was preforming the parking flow the aircraft experienced a transient parking brake fault. After I checked the triple indicator for sufficient pressure the parking brake was selected on; seat belt sign was turned off; and while as I was reaching to turn off engine #2 the parking brake fault" ECAM illuminated then went off. I then noticed and felt the aircraft moving. I immediately pressed hard on the brake pedals; and the aircraft came to a stop after moving approximately 6-7 feet. A normal shutdown and parking checklist was then completed. The ground crew then preceded to hook up the tow bar and tug to reposition the aircraft back to a normal position. The station manager; as well as the ground personnel were briefed on what happened; and for the reason of the forward movement of the aircraft after we were stopped. I called dispatch to advise them of the situation; as well as Maintenance Control. A logbook entry was completed; the outbound crew was briefed; as well as the out station maintenance tech who showed up to aircraft as well were leaving. The aircraft was then removed from service."