Hi Zeldazog, you car from your discription is a Clio2 Phase1 and at that age its usually a Cobra 8265 thats fitted, well the ones I've seen (factory and upgrade models).
The purplish dome on the roof console is the PLIP IR receiver (yes its easy to replace and its not coded to the car, so getting one from a breakers is no problem, cost ... I have no idea) ... it works the remote locking and the remote alarm arming and disarming. .... (does the alarm arm when you press the central locking button on the floor console ... it should ... that should let you see it the alarm is arming or not, even if the remote locking is not working)
I guess its a replace to try ... it can be easily damaged if the car has had a water leak ... the radio antenna base is a common water ingress point and its right above the IR reciever. If there are signs of a water leak this could be your problem.
Should it be leaking, get it sealed with clear silicone, so it causes no further issues, esp. if you change the IR receiver.
Double check the keys esp the position and condition of all the contacts of the circuit board (make sure it fits snuggly into the clear rubber lining in the key and the microswitch under it ... also all the battery contacts in the key as they are all troublesome when they get older .... also make sure the batteries are the correct way up.
Lets know how you get on ... I hope it works for your situation.