The bill, dubbed The Creation and Internet bill, passed 296 to 233 and will now head to the Senate on Wednesday for final approval.
The three strikes laws would work as follows: A new regulatory body would send alleged pirates a warning e-mail, then a written letter, and finally cut them off the Internet for one year for a third offense.
Critics of the bill have warned that the bill may lead to innocent people being punished, if their computers or networks are hacked.
The socialist Patrick Bloche adds that the bill is "dangerous, useless, inefficient, and very risky for us citizens".
John Kennedy, chairman of the IFPI, applauded the move, adding that the bill is "an effective and proportionate way of tackling online copyright infringement and migrating users to the wide variety of legal music services in France".