Captain reported a rejected take off due to an ECAM for ENG1 COMPRESSOR VANE. The aircraft returned to the gate for maintenance.

Narrative

Normal engine starts and had over 7 minutes run time on the second engine when we were cleared for takeoff. We were cleared for takeoff before we reached the hold short so we set up for rolling takeoff on Runway XXL in ZZZ. FO (first officer) was pilot flying so positively exchanged control of the aircraft and he smoothly ran the thrust levers up to FLX (Flex) and said Check Thrust. Both engines spooled up evenly. I said Thrust Set; but had noticed a faint; modulating sound as the engines spooled up. We were very light; TOW (Take Off Weight) around 130;000 pounds. The lower FLX power setting caught my attention as well as the initial; modulating sound so I stayed on the engine instruments longer than normal. As I was transitioning my scan to the airspeed; we heard the chime. Went back to the engine instruments and we had an ECAM (Electric Centralized Aircraft Monitor) for ENG1 COMPRESSOR VANE. I initiated the reject; initially going into reverse and almost simultaneously the MAX auto brakes engaged. We are estimating the IAS was about 70 knots when the ECAM displayed. Once the MAX auto brakes engaged; I worked to get those off as I came out of reverse. We kept it rolling and made the call to tower and told them no assistance was required. FO (First Officer) made the Remain Seated call to the cabin. Tower told us to clear at taxiway and hold short. We complied and completed the RTO (reject takeoff) checklist and the ECAM which had us shut down ENG 1. I called the Flight attendants to let them know what had happened; then made a PA. FO called Maintenance and initially we thought about and discussed a tow in because of the max braking. I did not set the parking brake and held the right brake since the left side was hotter. We referred to the Brake Cooling Considerations in performance. The left brake max temp was 415 degrees. Coordinated with Maintenance; Ops; Ramp and Ground and since the brake temps were already decreasing we returned to the gate. When we got to the ramp area; they were set up to tow us into the gate. We referenced the Tow In checklist and we arrived at the gate about 25 minutes after the ECAM/RTO. Brake temperature was 310 degrees on the hottest brake when we set brakes at the gate.