In a letter addressed to French Prime Minister Manuel Valls, unions warned that they would take action unless the government enforced the ban UberPop, which puts non-professional drivers with their own cars in touch with passengers via their mobile phones or a website for rides at budget rates.
“The message is clear: 14 organizations, all of which are national federations and the Parisian unions give 15 days for UberPop to be banned,” Pascal Wilder, Secretary General of the National Federation for Independent Taxis was quoted as saying by Europe 1 radio.
“Today the government has the means to prohibit the secretive and illegal work, which is done by those drivers. There are laws for this and they are not being applied," the secretary general added.
UberPop is technically illegal in France, thanks to a new raft of laws brought in last year.
However the company is appealing a €100,000 ($113,000) fine it received last year.
The court of appeal has put back its decision until September meaning parent company Uber are still permitted to run the app.
However under the Thévenoud law introduced on January 1st French police are allowed to hand out fines if they catch the drivers. In the past three weeks alone around 250 Uber drivers have been fined, according to Europe1.
Last month French police raided the Paris offices of Uber as part of its investigation.
The company called the raid an "attempt at intimidation," adding that dozens of non-professional UberPop users had been fined since the start of the year.
Founded in 2009 and in operation in about 250 cities in 50 countries, Uber has become an object of scorn from traditional taxi companies fighting for survival.
In March hundreds of taxi drivers from Belgium and France brought central Brussels to a virtual standstill with their vehicles in a protest against the web-based Uber.
Around 100 French taxi drivers travelled to Brussels to take part in the protest.
It also emerged recently that Uber has filed complaints with the EU against France, Germany and Spain.
Uber's American founder Travis Kalanick has said the system will create 50,000 new jobs in Europe this year, and help take 400,000 cars off the road by encouraging drivers to use taxis instead of their own vehicle.