After reviewing evidence in the case of the alleged bite, including footage from several angles, the commissioner was "not able to conclude that any particular individual carried out an act of foul play", organisers said in a statement on Monday.
France scored a try 20 minutes after the end of normal time to seal victory after a bizarre end chaotic end to the game.
Furious Wales coach Rob Howley said replacement prop Uini Atonio's substitution by starter Rabah Slimani in stoppage time brought the integrity of the game into disrepute and there was evidence North had been bitten.
"I am sure you can ask George if you can have a look at his arm. There is evidence to suggest that there is a bite," Howley said after the chaotic game in Paris.
France coach Guy Noves responded angrily when a reporter suggested North had been bitten in stoppage time. Noves bit his hand and said: "Look, there's a bite mark, here."
Howley said France's late substitution was planned, suggesting Slimani should not have been allowed to come on again. He had earlier been replaced but was allowed to return when Atonio went off for a head injury assessment.
(Writing by Ken Ferris; Editing by Nick Mulvenney)
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