The court found that the couple received rent from a company called Jalons, set up by Tellenne, also known as Basil de Koch, to publish humorous journals.
The couple have four months to leave their two-storey home, which consists of two apartments knocked together, thanks to a ban on evictions during the winter but must also pay 1,500 euros to the council.
The couple's lawyer, Laurent Créhange, claimed that the city council had previously agreed to the flat being used as an address for the company, which, he said, was not a commercial concern.
They claim that the case is a political vendetta.
Communist city councillor Ian Brossat, who tipped off the housing department about the case, hailed the decision.
"Nothing could justify Mme Barjot, who by the way owns several properties, occupying social housing, given her family circumstances," he said.
Barjot owns a four-room Paris apartment that she inherited from her mother, another in the city's 15th arrondissement that she inherited from her father, a holiday home near Saint Tropez on the riviera, a house at Trouville-sur-Mer on the Channel coast, three cellars in Paris and a garage, according to Le Parisien newspaper.
The city's housing department earlier tried to raise the 2,850-euro monthly rent but the couple fought off the bid, claiming that they were entitled to a below-market-value rent due to their annual income of 36,000 euros.