Wales were crowned Guinness Six Nations champions after France lost 27-23 to Scotland.
Les Bleus required a bonus-point victory and a winning margin of at least 21 points from this evening's rearranged clash with the Scots to snatch the title but they fell short.
The result in Paris was welcome news for the Welsh, who claimed Championship glory for the second time in three years.
Wayne Pivac's men had been forced to wait an additional six days to discover their fate after the heartbreak of Saturday's last-gasp 32-30 defeat at Stade de France denied them a Grand Slam and gave the French renewed title hope.
Success marked a remarkable turnaround for head coach Pivac, who faced questions about his future having finished fifth in last year's Six Nations after succeeding fellow New Zealander Warren Gatland following the 2019 World Cup.
Wales won just three of 10 Tests in 2020 and were unfancied ahead of the tournament.
But, after edging past the 14 men of both Ireland and Scotland, a 40-24 success over deposed champions England and a routine win against Italy were ultimately enough to hold off the challenge of Fabien Galthie's talented French side.
The result means that Ireland finish in third place, which is worth about €2.5million in prize money, staying just ahead of Scotland on points difference.
Wales coach Wayne Pivac said his players were "over the moon".
Pivac told BBC Sport: "What a tournament it has been and, from a Welsh point of view, we are over the moon. We are very happy to have won the championship."
He added: "It's a shame we couldn't have done it together as a group last week. We felt we did quite a bit in the game to win it but it wasn't to be.
"It doesn't take away from the fact a lot of hard work has been done and we've come out on top of the points table and won the tournament.
"Some great rugby has been played in this tournament and it is exciting times for all concerned.
"It was a hell of a game, wasn't it?
"It reminded me a lot of last week, with cards and people coming and going, penalties and missed opportunities. It had everything and it was a great game to watch. What a tournament it has been."