The announcement was made by billionaire founder Xavier Niel on Tuesday.
He took to the stage at a morning press conference packed with flashing lights and cheering fans, dubbed a "show à l'américaine" by one newspaper.
Niel promised a tariff of €19.99 ($25.50) per month offering unlimited calls and texts and free calls to 40 countries in Europe and North America.
"You're being squeezed like lemons," he said, in a reference to the current three operators, Orange, SFR and Bouygues.
"If you want to stop paying too much, leave your operator or ask them to match our prices," he said.
France is one of Europe's most expensive mobile phone markets. A similar offer at France Telecom's low-cost service SoSh costs €49.50.
Le Parisien newspaper reported on Wednesday that just one hour after the announcement 1.8 million people had been in touch with the company about the offer.
Despite his attack on rivals including Orange, owned by France Telecom, the service will use the France Telecom network for about 70 percent of its mobile network. It has pledged to invest in its own network.
The company's share price was up 2.81 percent on the news.