The last five minutes of the game, which took place in the southwestern Japanese city of Oita, decided the winner with Wales scoring the decisive point late into the match, Efe news reported.
The first try was scored by France in the fourth minute through Sebastien Vahaamahina while Romain Ntamack failed to convert, leaving the score 5-0 in France's favour.
The Les Bleus did not take much long to score their second try by Charles Ollivon in the eighth minute and Ntamack successfully converted this time.
With the score 12-0 in France's favour, Wales stepped up in the 12th minute when Aaron Wainwright took advantage of an error in the French defence and scored the team's first try to bridge the gap with five points.
In the 19th minute, Wales' Dan Biggar scored from a penalty to reduce the gap to 10-12.
In the 30th minute, South African referee Jaco Peyper showed a yellow card to Wales' Ross Moriarty, who had just entered the field replacing Josh Navidi.
Wales were left without a player for 10 minutes, easing the way for France to score a try by Virimi Vakatawa in the 31st minute. With Ntamack's conversion, France led 19-10.
Shortly after the start of the second half, France lost Vahaamahina, who was shown a red card for grabbing Wainwright's neck and hitting him on the jaw with his elbow.
Biggar again reduced the gap for Wales to 13-19 with a successful penalty conversion in the 53rd minute.
The game entered a phase strong physical rivalry, but Wales' pressure paid off in the 74th minute as Moriarty managed, after a fight for the ball, to score Wales' second try as Biggar converted to take a 20-19 lead with just five minutes remaining on the clock.
Les Bleus tried to add some additional points, but failed and were eliminated from the World Cup. In the semifinal, Wales will face the winner of the last quarterfinal match between hosts Japan and South Africa.
In the previous eight editions of the Rugby World Cup, Wales had reached the last four stage twice in 1987 and 2011.
( With inputs from IANS )