Cane sustained a head cut during the recent win over Ireland and will need to undergo Head Injury Assessment protocols, while Tele'a is dealing with an injury to his hand.
Shadow All Blacks XV captain Du'Plessis Kirifi will join the team, along with winger Chay Fihaki and lock Fabian Holland, who replaces Sam Darry following the latter's season-ending knee injury.
New Zealand will face France on Saturday at Stade de France.