The administrative tribunal found that Jean-Pierre Brard, the communist mayor of the eastern Paris suburb of Montreuil-sous-Bois, was wrong to have issued a municipal decree last year forbidding the show.
It ordered him to pay 750 euros (900 dollars) to the company that tried to organise the event, Jasmeen.
"This decision constitutes a legal victory over the recurrent arbitrary decisions of some elected officials and public services towards the Muslim community," one association, the Collective Against Islamophobia in France, said in a statement.
France counts Europe's biggest Muslim community, estimated to be nearly 10 percent of the country's 60-million-strong population.