"at 0155 the Captain woke the second co-pilot and said '[...] he's going to take my place'".
The 'second co-pilot' presumably was the junior FO.
Not necessarily, the transcript says "le commandant de bord réveille le second copilote" which seems to me to read he woke the second, or
other P2.
So reading the BEA transcript it's quite possible that the junior P2 was in the RHS from takeoff. The captain woke the other (or second) co-pilot by some means and then commented to the junior pilot in the RHS that:"he's going to take my place". i.e. the senior P2 simply replaced the captain in the Left hand seat.