The bill has proved to be very controversial, and even though French President Nicolas Sarkozy has been in support of it, the bill was nevertheless rejected by the French Assembly last month.
The music industry worldwide has been calling for legislation to tackle the problem of piracy on the Internet that has been costing them a lot of lost money.
The bill was approved by 296 to 233 votes by the lower house on Tuesday and has now also had its final approval by the French Senate.
Although the music and film industries welcome the new bill some consumer groups are not happy with it because they claim that innocent people can become the victims of hackers and then prosecuted under the new laws.
