First Officer reported receiving a cargo door open ECAM after takeoff. Flight crew returned to departure airport and performed an overweight landing.

Narrative

After takeoff and gear up we got an fwd cargo door ecam. The message told us to limit our altitude to less than 10;000ft. We preformed the ecam actions and immediate checklist. We decided to level off at 5000 feet while we made our decision. We got delayed vectors. There were no other indications that the door was open but due to the fact we didn't have the fuel to make it to ZZZ1 [airport] with the fuel on board we decided to return to ZZZ and get it fixed. The pilot monitoring (captain) set it up the aircraft for a return to ZZZ [airport]. We did all the checks and briefs; and we knew we were going to have to do an overweight landing. Did the overweight landing checklist. The captain decided he would do the landing feeling with his experience; he would have more control on touchdown. We transferred control and got vectors back for the ILS XXR. We landed with a light touchdown and taxi back where we wrote up the maintenance issues for both door issue and overweight landing issues. Sensors fail unsure what we could've done to prevent that.