It seems more and more likely that the AF crew on that fateful night were routinely picking their way around CB cells in the ITCZ, like all airline pilots do on a regular basis, when they unknowingly flew through an air mass that contained enough ice particles to disable all pitot probes.
The resulting effects of such failure at high altitude, as documented earlier in the thread, are quite dramatic on the flight instruments and may have led to a rapid loss of control of the aeroplane.
Since the crew primary task then, is to try to regain control before anything else gets done, it is not surprising that distress calls were never made.