The draft law - which also introduces new penalties for music pirates - would force Apple, Sony and Microsoft to share proprietary anti-copy technologies so rivals can offer compatible services and players.
The National Assembly, France's parliament, approved the bill by 296 votes to 193 on Tuesday. The legislation has to be debated and voted on by the Senate - a process expected to begin in May.
Apple has declined to comment on the bill or on analysts' suggestions that the Cupertino, California-based company might choose to withdraw from the French online music market rather than share the proprietary technology at the heart of its business model. Representatives for Apple France declined to comment on Tuesday.
Under the bill, companies would be required to reveal the secrets of hitherto-exclusive copy-protection technologies such as Apple's FairPlay format and the ATRAC3 code used by Sony's Connect store and Walkman players.
That would permit consumers for the first time to download music directly to their iPods from stores other than iTunes, or to rival music players from iTunes France.
The bill states that such technologies must not pose an obstacle to interoperability between different systems, while granting them a firmer legal foothold.
Anti-copy devices on DVDs and other media had come under repeated attack in French courts for infringing on consumers' rights to make copies for fair use.
The new legislation would also introduce penalties ranging from $50 to $180 for those caught pirating music or movies at home and $4600 for hackers who disable copy-protection systems.
Those caught distributing software for online piracy face fines of up to $365,000 and jail terms.
Under the fast-track parliamentary procedure invoked by the government, the Senate debate is likely to be the last full reading of the new legislation.
If the Senate passes any amendments, a committee of politicians from both houses must be convened to thrash out a compromise text, which must then be formally approved in two final votes by senators and deputies from the lower house.