France scored a try 20 minutes after the end of normal time to seal victory after a bizarre end chaotic end to the game.
Howley said replacement prop Uini Atonio's substitution by starter Rabah Slimani in stoppage time was unlawful and that there was evidence Welsh winger George North had been bitten.
"The integrity of the game has been brought into disrepute," Howley told a news conference.
"What happened in the last moments of that game shouldn’t ever happen again. 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."
Slimani had earlier been replaced but he was allowed back on when Atonio went off for a head injury assessment.
Howley believes the substitution was planned, suggesting that Slimani should not have been allowed to come on again.
"Slimani warming up prior to him going back on. One of their coaches outside the technical area had a conversation with the doctor, and within a minute of it, the tighthead was taken off," Howley said.
"There is a technical area and you are not allowed outside that. Ultimately, someone has come outside that and allowed the doctor to go on at a break in play, which is outside the laws of the game."
Asked whether France had cheated, Wales captain Alun Wyn Jones said: "I would not use that word but I think there will have to be someone looking at it."
Read the full article on eurosport.co.uk: Wales fuming after controversial and chaotic France loss