A319 Captain reported the aircraft started rolling after parking at the gate. The parking brake had been set; but apparently failed; allowing the aircraft to roll back.

Narrative

We were marshaled into the gate and I set the parking brake which initially showed that it was set. Both engines were shut down when I noticed commotion outside the aircraft on the jet bridge. Then an ECAM came up that indicated the parking brake had failed and I realized the aircraft was moving forward; and the triple gauge showed no parking brake pressure. I braked manually to stop the aircraft then turned the parking brake off and then on again. The triple gauge showed normal pressure and the ECAM disappeared. I released the brakes and the aircraft remained motionless. I opened my side window and asked the agent if anyone was hurt or if anything was damaged. She said no one was injured and nothing was damaged but that the aircraft would have to be hooked up to the tug and pushed back so the jet bridge could be mated with the aircraft. I made a PA to the passengers and sat everyone back down while we reposition the aircraft. Deplaning was normal after that. Transient parking brake failure.