A320 Captain reported a Skin Valve Fault on ECAM after departure. The flight crew ran the QRH and checklists. The aircraft would not pressurize correctly so The flight crew requested vectors and performed an air turn back to the departure airport.

Narrative

After departing ZZZZ we received a Skin Valve Fault on ECAM. FO on his third flight of IOE continued to fly the airplane and communicate with ATC. We completed the after takeoff checklist followed by the ECAM and QRH. ATC was notified we needed to stop our climb at FL100 to troubleshoot a pressurization issue. The ECAM actions did not rectify the pressurization problem. Dispatch and Maintenance were contacted via SAT COMM. Maintenance verified we had completed the ECAM and asked us to cycle both the inlet and extract override push buttons. The ECAM and QRH actions did not solve the issue of the aircraft not pressurizing. Between myself Name and Dispatch a decision was made to return to ZZZZ. We asked to hold at the IAF and informed ATC that we would be returning to ZZZZ. At this point the Flight Attenmdents (FA) and passengers were informed that we would not be able to go to ZZZ and would be returning to ZZZZ. In the holding pattern I set up for the approach to Runway XX and completed the overweight landing checklist. After briefing the approach we completed the RNP uneventfully. After landing and turning off of the Runway we received a OFV not fully open ECAM. One thing I could have done better in this event was verify the OFV was fully open. In the ECAM actions one of the steps was to select MAN pressurization and hold the VS to the full up. I did this however I was of the impression that full up meant to equalize the current pressure altitude to the cabin altitude. Upon selecting full up the cabin immediately went to our current altitude. I thought I had held full up long enough. The cabin altitude in the airplane during the decent was equal to the outside altitude. After landing and the OFV not fully open ECAM I selected MAN VS up for a few seconds and the ECAM went away. We were at sea level cabin altitude upon landing but the OFV wasn't 100% open. We taxied to the Gate and wrote up both the overweight landing and the skin valve fault.