Incorrect. Co-Pilot No2 was PF starting 1:55 according to BAE report may. Taken from the CVR. He took over Captains seat, left at 1:59.
Quote:
A 1 h 55, le commandant de bord réveille le second copilote et annonce « […] il va prendre ma place ».
First, "Prendre ma place" can refer simply to the captain's physical position, ie his seat, not necessarily to his role.
Second, you forget that the captain was PNF. So even if the new arrival did take over the captain's current role, he would have become PNF.
There's enough ambiguity in the French version that your interpretation is possible, but to this native French speaker it seems more natural to read the report as saying that the initial PF remained PF.
Note, for example that it is the PF that conducts the briefing for the new arrival.