French government spokesman and Budget Minister François Baroin told France Inter radio the law was "incompatible with the application of ideas on press freedom that have been validated in European treaties".
Several EU members have criticised Hungary over the law, which calls for a new media authority, dominated by appointees of the ruling Fidesz party, to oversee all public news production. It can also levy big fines on private media, which are required to be "balanced".
'Put the law between parentheses'
Hungary has been publicly rebuked by the UK, Germany and Luxembourg, whose foreign minister questioned whether Hungary was worthy of leading the 27-member bloc.
"France's position [and] the position of all EU member states needs to be strong enough in diplomatic and political terms so that Hungary's government can have a more serene presidency by putting this law between parentheses," Baroin said.
Budapest said it was confident that the regulation "complies with the relevant EU standards in all respects".
In France, the law has drawn criticism from across the political spectrum, with the main opposition Socialist Party labelling it "a very bad sign for Europe and for the liberty of the press".
The controversy over the media law has contributed to a growing cloud over Hungary's EU presidency.
Budapest and Brussels have clashed several times since Prime Minister Viktor Orban rejected austerity measures, cut ties with the International Monetary Fund and opted for unorthodox fiscal steps to cut the budget deficit and boost economic growth.
The European Commission announced on Monday that it was investigating the legality of crisis taxes imposed by Hungary's centre-right government on the telecoms, retail and energy sectors.
(EurActiv with Reuters.)