Captain reported full Left Pedal was required to maintain runway center line during take off. After take off; when the gear handle was raised to up; the Landing Gear would not retract. The flight crew performed an air turn back and precautionary landing at departure airport.

Narrative

On takeoff roll the aircraft required almost full left pedal to maintain center line at lower speeds; as I was about to reject the takeoff the rudder authority began to compensate; and the aircraft went back to feeling normal. The aircraft pulling to the right was a previous write up in the Aircraft Maintenance Logbook (AML) which I had expected on taxi but not takeoff. After takeoff when I directed the gear up the First Officer (FO) was unable to move the landing gear lever and we had an ECAM of L/G Shock absorber fault. As we continued to climb the malfunction escalated when I brought the thrust levers to Climb and the Auto Thrust kicked off. We were also unable to engage the Autopilot and had another ECAM of auto flight auto thrust off. We promptly [requested priority handling] and asked for vectors back to ZZZ. I had a Jump Seater who is also an Airbus Captain and brought her into the loop. We completed the ECAMs and follow ups then I determined we needed to burn off fuel to avoid an overweight landing which would require vectors for approximately 15 minutes. The Jump Seater offered to make the PAs; coordinate with the Flight Attendants; and call to arrange a gate which greatly reduced my workload since myself and the FO were flying raw data while also troubleshooting and coordinating with ATC and programming to return to base. I was very concerned that upon landing I would lose control authority because of my experience on the takeoff roll and the history of the aircraft pulling to the right so we discussed this possibility and what to expect. We were able to land and return to the gate without further incident; however I did speak to the Maintenance Team that met the aircraft and they mentioned that as soon as they jacked up the aircraft to inspect the gear the nose gear shifted and pointed approximately 7 degrees to the right instead of being in the neutral position. They said because of this the sensors would not align and the aircraft would not retract the gear and the computers assumed we had not left the ground which is why the automation and other systems would not work. This aircraft pulling to the right was a previous write up.Maintenance could have dug further into a repeat write up. I could have committed to rejecting the takeoff as soon as I noticed directional control issues.