Thx for your answers !

Yes I use an OMTP adapter : this one !
But as I said before, it doesn't make my standard computer headset work.

Why is there a list of compatible headset ?
If the phone follows the OMTP standard, with the appropriate adapter, every headset should work, shouldn't it ?

And an additionnal question : is it possible the problem comes from the TV-out signal ?
(I don't even understand on which part of the jack, the TV-out signal pass through).