Referee Wayne Barnes asked television match official Peter Fitzgibbon to check the incident, but he could not find any clear footage so the game resumed without action being taken.
Citing commissioner John Montgomery was also unable to find clear evidence.
But there could be action taken over France's replacement of Uini Atonio.
Wales coach Rob Howley said he was left to "question the integrity of our game" after France replaced prop Atonio with Rabah Slimani during the 20 minutes of added time that were played.
France's team doctor said Atonio needed to go off for a head injury assessment.
Six Nations Rugby said it was "aware of concerns" about the incident and "is looking into the matter", but no action would be taken over North's allegation.
A statement read: "Based on the information available to him in the case of the alleged bite (including footage of the incident from several angles), the citing commissioner has not been able to conclude that any particular individual carried out an act of foul play, and accordingly he has not made a citing complaint ahead of the ordinary deadline for doing so, ie within 48 hours after the conclusion of the match.
"While the relevant rules provide that in certain circumstances, for example where the citing commissioner is uncertain as to the identity of the player(s) concerned, he is permitted to make a citing complaint after the 48-hour deadline, Six Nations Rugby anticipates that this will be the end of the matter in terms of the alleged bite."
Six Nations officials will not take any action over an alleged bite on Wales wing George North during Saturday's 20-18 loss to France.