For info, from what I have understood of the new French law:
1-Media companies will pay other companies to track IPs of people using P2P network to share pirated content.
2-The list of Ips will then be sent to an independent regulatory commission(Hadopi, same name as the law).
3-Warning will the be sent to people with the IP on the list.
4-If someone IPs is caught a third time, the person is prosecuted in court of law.
5-If the person is found guilty, the ISP is asked to cut the internet connection of this person.
6-the person could be charged for sharing pirated content(money and may be jail) and still have to pay the remaining of its internet subscription until the end of its contract with the ISP (or 1 one year, I can't remember) and can not take another subscription with an other ISP.
Another thing, it seems that to prove that you are not guilty if your IP is on the black list(like someone pirated your wifi), you'll need to have installed(and bought form the commission) a spyware on your computer that analyses what you do with your internet connection.
Things may have been changed a bit these last weeks to force the passing of the law but that is what it seemed to be few weeks ago.
ps: Sorry if I made some English language errors.