Air carrier Captain reported a main cargo door open ECAM warning at cruise. The flight crew elected to divert and make a precautionary landing at the diversion airport.

Narrative

We operated Aircraft X from ZZZ to ZZZ1. Departing Runway XX; shortly after rotation we had a DOOR AFT CARGO ECAM caution. I requested with ATC to level off at 5;000 ft. to trouble shoot the condition. After performing ECAM actions; the indication did not go away. We noticed a low cabin pressure but it was due to the low altitude as well. The First Officer (FO) checked information for our situation. At that point we could not determine if the cabin would hold pressure or if the cargo door would remain closed. Considering the flight was a trans con of 5:40 min; I decided the safest course of action was to divert to ZZZ2. I requested priority handling and proceeded to ZZZ2. The FO performed an Over weight Landing Checklist on the QRH as well as landing Data for Runway XXC. I landed the aircraft as smoothly as possible due to the heavy weight (195K Lbs.) No over weight landing faults were recorded or over heated brakes conditions were noted. After clearing the Runway; the emergency ground personnel inspected the door and found no damage. At that time proceeded to the gate and maintenance was notified. Maintenance in ZZZ2 never opened the cargo door to inspect locks or sensors.