A320 Captain reported Forward and Aft Cargo Compartment Smoke Detection Faults climbing through FL360. The flight crew ran the QRH and check lists. Priority handling was requested and the flight crew performed an air turn back and precautionary landing at departure airport.

Narrative

ZZZZ RETURN.Operating Aircraft X; from ZZZZ to ZZZ. Climbing through FL360; we received a Forward and Aft Cargo Smoke Detection Fault. We reviewed the QRC and QRH. We completed QRH XX but it was only for the Forward or Aft and not Both Cargo Compartments; and I wasn't sure but I also thought I smelled something burning. I called; Dispatch and Maintenance (via SATCOM) for some guidance. Maintenance lead me to XY; a different QRH checklist which directed us to land ASAP; and Dispatch told us to return to ZZZZ.In the heat of the moment I was wrapped around my return to ZZZZ that the remaining checklist was not completed; I believe that Maintenance misunderstood my situation and that was not the right checklist to begin with.We notified ATC and [requested priority handling] immediately. The crew was given a briefing code which later changed to lower code just prior to the final approach. After landing safely in ZZZZ; Crash Fire Rescue (CFR) conducted an inspection of the aircraft prior to taxiing and additional inspections of the cargo compartments and interior of the aircraft after parking; and no issues were found.Forward and Aft Cargo Compartment Smoke Detection fault climbing through FL360 was put into the aircraft logbook.