Consumer groups warned the new law could punish the wrong people
The French National Assembly will vote on Tuesday to decide whether to allow the authorities to cut illegal downloaders off from the web.
The hard-line policy has drawn worldwide attention as nations around the globe grapple with the issue of piracy.
An earlier version of the bill was ruled unconstitutional and a compromise version has been hammered out.
The legislation is backed by President Nicolas Sarkozy.
The proposed legislation operates under a "three strikes" system. A new state agency would first send illegal file-sharers a warning e-mail, then a letter and finally cut off their connection if they were caught a third time.
While it is backed by the film and record industries, consumer groups have warned that innocent people may get punished.
The European Parliament is currently considering whether cutting off internet access is a breach of human rights.
In the UK, Business Secretary Lord Mandelson has been widely credited with seeking a tougher line on UK piracy laws.
The British government is proposing a tougher stance which could include cutting repeat offenders off from the net.