During the game, PSG supporters unveiled a massive 85-foot banner that said some less than nice things about people from the northeast of France, where Lens is located.
The Parisians called their countrymen, "pedophiles, unemployed, inbreds."
PSG had asked the French National Olympic Committee to help overturn the verdict, but the French soccer federation stood by its ruling. Federation president Jean-Pierre Escalettes defended the decision.
"PSG aren't being picked on but we had to remain firm faced with something that misrepresents the sport," he said. "We think it's a suitable sanction. At the time we were accused of being lax and now we're told it's too severe."
The League Cup victory was a bright spot in a poor season for PSG. The club flirted with relegation for most of the campaign before finishing the season in 16th place.