Ruud, who had reached the quarter-finals at Bercy in 2021, will face the Italian Lorenzo Musetti (23rd) or the Georgian Nikoloz Basilashvili (106th) to try to find this stage of the tournament.
Gasquet started the match full of good will, hitting his opponent on the second point of the game with a magic backhand he has the secret to and which hit the mark along the line.
But very quickly, Ruud completely stifled Gasquet's offensive inclinations, dominating him in all areas of the game to soar 5-0 in the first set, leaving the Frenchman only five points in as many games.
Gasquet then won his first game before conceding the first set on a shutout for Ruud.
The game evened out in the second set.
Each player won their face-off until Gasquet broke the break to lead 5-3 and serve to tie a set all.
But he made a bad service game and let Ruud break.
The two men thus reached the tie break.
The Frenchman quickly took the lead to lead 4 points to 1, but Ruud came back to 5/5 and offered himself a first match point at 6/5.
His potentially winning long-line shot landed ever so slightly in the lane, as evidenced by footage from the Hawk Eye verification system.
The Norwegian got a second match point at 8/7 and this time converted it by taking advantage of an unforced error from Gasquet.