Air carrier Captain reported while attempting to park at the gate the parking brake was set but the aircraft began to roll resulting in the flight crew applying the brakes and resetting the brake.

Narrative

Upon arrival at the gate and after setting the parking brake; I check the Brake and Accumulator pressure indicator and it indicated the brakes were set. I commenced my shut down flow and while my head was down selecting the #2 Eng Master switch to off; my First Officer (FO) saw that we had begun to roll. He gasped and applied the brakes through the rudder pedals. As this was happening; the ECAM announced a Park Brake Fault. I applied the brakes on my side also and reset the parking brake and slowly released the brakes to see if they were holding. The triple indicator displayed it was holding pressure. Once the aircraft was shut down and checklist complete; I wrote the fault in the logbook and spoke with Maintenance about the occurrence. No damage to the aircraft occurred.Cause: There are no causal factors other that a mechanical malfunction as Maintenance found a faulty part and replaced it. The one thing I would do differently is ensure the aircraft was properly chocked before releasing the brakes a second time and I would have spoken with the crews chief to ensure no one was hurt and that they were aware of what had just occurred.