The iPod maker would ultimately have to choose between making iTunes downloads compatible with rival platforms or pulling out of France if, as expected, the parliament in Paris approves a draft copyright law, according to the report.
The law would also allow rivals to serve up tunes to iPod users through their own online music download services.
Digital Rights Management (DRM) software embedded in tracks downloaded from Apple's iTunes Music Store prevents them from being played on digital music players other than an iPod, but the French bill seeks to impose "interoperability" on online music stores and break Apples closed system.
"It is unacceptable that... the key should be controlled by a monopoly. France is against monopolies," Martin Rogard, an adviser at the French Culture Ministry, told The Financial Times. "The consumer must be able to listen to the music they have bought on no matter what platform."
Rogard said it was "desirable" that France led in this respect, but hoped that it was the start of a Europe-wide move to open up digital music.
However, opponents of the draft law say forcing Apple to admit competitors to a market it was instrumental in creating is sending the wrong signal to technology companies.
CompTIA, a trade association, reportedly said the law was the latest in a series of measures in the European Union that were "punishing inventors and stifling innovation."
Apple is reportedly waiting for the law to be passed before making any comment.