The French ruling majority UMP party voted in favour of the bill, however, the Socialist Party say that they will be appealing to the Constitutional Court once more.
An earlier version of the Internet piracy bill had been ruled as unconstitutional and a compromise had to be found.
The law will, however, only become officially valid if a special commission can decide on a new wording in the next few days.
French President Nicolas Sarkozy is reported to have given his support for the bill, in which it is proposed that a new state agency would send illegal file-sharers an e-mail caution, then a letter, and finally to disconnect them if they were found guilty of Internet piracy for a third time.
