Thuram was a CB when he played for Monaco and RCB. On a practical note, RCB is really a CB, that concentrates on man-marking.
The reason he played RB for France, IMO, is that French already had Desailly (A terrific player in his prime) and Laurent Blanc (Ditto), and they formed tremendous partnership so basically there was no room for Thuram to play in that position.
If anything, with loss a yard to two in pace, I think Thuram is better off playing CB than as a full-back right now.