The AFP report said the surprise decision, adopted 30 votes to 28, runs counter to moves in most other Western countries, where legislators are seeking to stamp out copyright violations via the Internet by declaring such downloads illegal.
The measure, introduced as two amendments to a government bill designed to toughen digital copyright protection, would deem that downloading copyrighted files is legal as long as it is for private use only and the downloader pays a general fee for royalty payments, the AFP report said.
The report said such a fee could, for instance, be added on to the monthly subscription charge for broadband Internet access at the cost of a few euros.
The measure in any case would have to pass the Senate and again the lower house before it becomes law.
Some French entertainers, though, raised an outcry over the parliamentary vote, fearing their livelihoods would be threatened if it becomes a law, the report said.