The report from the French telecoms federation (FFT) was leaked by the site owni.fr and reported in Sunday's Le Parisien newspaper.
The move is apparently aimed at helping manage the flow of internet traffic. It is estimated that 5 percent of customers use around 80 percent of bandwidth.
France currently has a large number of internet offers that provide unlimited use of the internet for prices that are among the lowest in the world.
Bundled packages offering telephone, television and unlimited internet are available from the major operators for between €32 and €38.
There are 21 million high-speed internet connections in France with the main providers being Bouygues, SFR and France Telecom-owned Orange.
Yves le Mouël, head of the FTT, told AFP that there was "no question that unlimited internet will be ended."
However, he confirmed that a study was under way on how to separate high-volume and low-volume users. France Telecom confirmed they were looking at "how we segment our offers."
French consumers have become used to offers that do not impose limits on how much bandwidth they can use and consumer groups were critical of the moves.
Consumer group UFC-Que choisir said limiting access to unlimited broadband was "unacceptable" and "without any economic justification."
A spokesman for the organization, Edouard Barreiro, said the objective of any changes will be to raise prices for most people.
"The only thing they want is to make more money," he told radio station Europe 1 on Monday morning. "Internet providers want their market to look like the mobile phone market with a multitude of offers and a huge range of options."