The FAA report[1] gives a more comprehensive description of events.
The pitot tubes had differential icing, and didn't all read 0kts – they reported different velocity against each tube, such as 40kts or 60kts (against an expected baseline of ~ 275kts). The computer correctly recognised the data was invalid and rejected it.
It's a common narrative that the captain immediately figured out the issue. The report and transcript of the cockpit recording[2] notes that the captain's interventions showed that he had not identified the stall, nor had the copilots.
~ cockpit recording ~
0:00 autopilot disconnects
0:01 [copilot right] "I have the controls"
0:11 [copilot right] "We haven't got a good display of speeds"
1:26 captain enters cockpit
1:30 [copilot right] "I don’t have control of the airplane at all"
1:38 [captain] "Er what are you doing?"
3:37 [captain] "No no don't climb"
4:00 [captain] "Watch out you’re pitching up there"
4:02 [copilot right] "Well we need to we are at four thousand feet"
4:23 ~ recording stops ~
[1] https://www.faa.gov/sites/faa.gov/files/AirFrance447_BEA.pdf
[2] https://bea.aero/uploads/tx_elyextendttnews/annexe.01.en.pdf