The rights of content creators are under threat, "in France and throughout the world", an open letter published in the Journal du Dimanche weekly says.
Several of Nyssen's predecessors, including Socialists Jack Lang and Aurélie Filipetti, joined her in signing the letter, as did musicians, film-makers, writers, actors and the bosses of several media organisations, such as Agence France Presse, France-Télévisions and Radio France.
The European Commission directive is to face a vote in the European parliament this week, after being rejected in July.
It would force internet platforms to reach agreements to pay content creators for their work when it is posted online.
If there is no agreement, they would have to set up a filter, as some platforms, such as YouTube and Google, to block content that is not covered.
It also proposes that platforms like Google News pay news media for posting their articles.
Euro-MPs report an unprecedented lobbying effort by the web giants, French MEP Virginie Rozière reporting that she received more than 40,000 emails on the subject in the run-up to the July vote.
"The only equivalent I've had was for firearms," she told France Inter radio.
Internet freedom campaigners also oppose the proposals, arguing that it will hamper creativity on the web, effectively banning memes and other adaptations of already-existing content.
Another open letter, this time against the plan, was signed by 200 academics who argued that it would restrict the availability of information.
Sunday's open letter was not the first in favour, another signed by 70 artistes preceded it and Paul Macartney wrote an email to MEPs urging a yes vote.