Hansen has called in locks Luke Romano and Tom Franklin and flanker Matt Todd into the squad as cover.
The All Blacks were always going to be without captain Kieran Read, who is still recovering from back surgery, but the number eight has been joined on the casualty list by a handful of other first-choice players.
The latest was Brodie Retallick, who suffered a pectoral injury playing for the Waikato Chiefs in Super Rugby on Saturday.
Chiefs coach Colin Cooper said the injury was serious and Retallick was unlikely to face the French in Auckland on Saturday.