Assistant coach Scott McLeod told New Zealand media that Barrett had missed training with a knee injury and needs to prove his fitness for the match in Paris.
"He's got a niggle in his left knee," McLeod said at New Zealand's training camp in Lyon late Monday.
"We will just wait and see how he responds today and tomorrow to a little bit more treatment."
Barrett is a first-choice starter for the All Blacks alongside Rieko Ioane (26). Anton Lienert-Brown (28) or David Havili (28) will deputise if Barrett is ruled out.
New Zealand are already without injured lock Brodie Retallick (32), loose forward Shannon Frizell (29) and prop Tyrel Lomax (27) for the France Test.
With Retallick sidelined by a knee injury, Scott Barrett is set to partner Sam Whitelock in the second row.
Frizell's hamstring injury means either Luke Jacobson or Dalton Papalii will start at flanker.
Fletcher Newell is set to prop for Lomax, who suffered a deep gash to the leg in a warm-up defeat to South Arica.
France also have also been hit by withdrawals. Lock Paul Willemse and fly-half Romain Ntamack have both been ruled out of the tournament with injury.
Prop Cyril Baille is unavailable for the start of the competition because of a calf injury while centre Jonathan Danty (thigh) is doubtful to face the All Blacks.
