Valls is seen coming top in the Jan 22 first round vote with 37 percent, ahead of second-placed Benoit Hamon, the former education minister, who is set to win 28 percent, and third-placed Arnaud Montebourg on 24 percent, the poll by Opinionway showed.
He would go on to win the left-wing ticket by beating either of these two opponents in a run-off second round vote on Jan 29, with 51 percent of the vote, according to the poll, although the margin of error in the second round is between 1.9 to 4.5 percent.
However, Valls drops three points from a similar poll earlier this month, with Hamon losing one and Montebourg gaining three in the survey of 536 people.