The move could affect access to video-streaming platforms such as Netflix and YouTube as well as Facebook, the world's biggest social network.
"We're entering an exceptional phase which brings us to take a close look at the (traffic) peaks to which we have become accustomed," Arthur Dreyfuss, the head of France's telecoms lobby FFT, told Reuters by telephone.
"We are entering an era of collective social discipline, which must be accompanied by digital discipline on the part of the telecom operators."
On an average evening, YouTube, Netflix and Facebook take on average about 80% of the overall internet bandwidth provided by France's four telecoms operators Orange, Altice Europe's SFR, Bouygues and Iliad, an industry source said.
France has shut shops, restaurants and entertainment facilities with its 67 million people told to stay home to help fight the rapid acceleration of the coronavirus in the country.
Schools and universities are also closed.
By Mathieu Rosemain