The clock showed 99 minutes and 55 seconds when France's replacement flanker Damien Chouly touched the ball down after nine penalty scrums and Camille Lopez slotted over the conversion to seal victory for the hosts.
France felt the game should have been brought to a close sooner with a penalty try as Wales were repeatedly penalised at the scrum, while the visitors focussed their ire on a substitution they said damaged the game's integrity.
In failing to award a penalty try, France coach Guy Noves claimed the English referee fell into a trap of his own making, while lock Yoann Maestri lashed out at the official.
"We were refereed like a small team and it's very painful. Barnes told me that we were not dominant enough in the scrum. But the Welsh were rigging every scrum," Maestri said.
"They were letting themselves get turned. It's down to the referee to spot it."
Maestri added that Barnes's failure to award a penalty try showed he had lost control.
"It was verging on nuclear warfare on the sidelines and the referee didn't react," he said.
France forwards coach Yannick Bru, however, was pleased his players did not let frustration get the better of them.
"I knew that Barnes, whom I've gotten to know over time, would not award a penalty try. But my players did not make any mistake," he said.
"We were more stubborn that Mr Barnes."
Wales were equally upset in the aftermath, however, accusing the French of making an unlawful substitution, which coach Rob Howley said brought the game's integrity into disrepute.
Starter Rabah Slimani was allowed back on as replacement prop Uini Atonio was taken off for a head injury assessment. Howley said he believes the substitution was planned.
"What happened in the last moments of that game shouldn't ever happen again," said Howley.
"One of the coaches had a word with their doctor and within a minute of that their tighthead went off. The evidence suggests that it's not in the integrity of our game."
Wales captain Alun Wyn Jones said: "I would not use that word (cheating) but I think there will have to be someone looking at it. They'll have to review that," said Jones.
(Reporting by Julien Pretot; Editing by Toby Davis)
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