I read NOT that they climbed, but they ascended, or, they were pushed, or, caught a severe updraft, and then wound up at 38,000 in a nose up condition, at below 60kts and thus literally out of control because at that time the controls would be inneffective.
As a previous post notes, the BEA report says that the PF pulled the stick back, resulting in the climb. It was not an updraft. Given the time the nose up command was applied, it was likely deliberate, meaning the PF wanted to pull the nose up. That does not necessarily mean he wanted to climb, but perhaps that he wanted to bleed off speed, or perhaps for some reason thought they were in a dive, and needed to pull the nose up.
The report is not that clear about how much time the pull-up lasted, nor how much time the PF later spent trying to push the nose back down again, so it is also possible that when the AP dropped out, the nose rose on its own, and the PF was trying to counteract that tendency, and was pushing down. I would have thought that the report would have mentioned that sequence of events if it happened that way, since it would have been readily seen on the DFDR. However, the report is very thin, so much could have been left out.
Will have to see the final report to see what might have given the pilot the impression he needed to pull the nose up, or if he was reacting to the effects of the AP dropout. That would also explain his mindset, and perhaps help explain why he didn't later put the nose down to recover, other than for a few short attempts.
The fact that the aircraft lost as much speed as they did also supports the fact that the the climb was due to a nose-up command, since it takes energy to climb, and if an updraft provided the energy, they wouldn't have lost as much speed as they did in the process.
Note that the aircraft didn't drop as low as 60 kts in the climb. That was an erroneous speed displayed in front of the pilot, and recorded on the DFDR, presumably as a result of the blocked pitot tubes. The report suggests that the aircraft's actual speed only dropped to about 185 kts, which is what two separate speed indicators said when they came back into correspondence, meaning the blockage in the pitots had likely cleared again at that point.