I think that your code is doing something wrong in the getter and setter of nomComposant and typeFile. Could you write them?, what is the scope of your bean and how are you initializing the nomComposant and typeFile variables?
In my opinion
you should remove the setPropertyActionListener, I think that you don't need them.
When you are clicking on commandLink "rejouer", first you are getting the value of nomComposant to assign it to nomComposantARejouer (getters and setter will be called before your code enter in rejouerMessage() method), maybe you can use directly the value of nomComposant in your backed bean when you are in rejouerMessage(), something like this: