http://www.bea.aero/fr/enquetes/vol.af.447/note29juillet2011.en.pdf
After reading the BEA report you URLed, I’m even more confused. The flight-control computer apparently switched to ‘alternate law’ software when they first lost the airspeed, and it’s not clear what algorithms that uses. However, it would still need good data from the ADS to fly the plane. I can’t help wondering if the low speed readings caused the FCS to go into landing mode, which would explain the nose-up inputs. It’s hard to see the pilots putting it into such a nose-up attitude (unless the HSI was bad).