Journalists' unions at Le Parisien newspaper accused their boss of self-censorship this week, claiming he had ordered critics not to review Merci Patron, "not even in 10 lines", and rejected a proposal by the politics desk to report on the "buzz" it had stirred up on the French left.
Arnault's LVMH, best known for its ownership of luxury brands such as Louis Vuitton, Sephora and Christian Dior, bought Le Parisien last year and the unions accuse editor Stéphane Albouy of not wanting to annoy his new boss.
Albouy called the film "dishonest" and accused Ruffin of manipulating the couple who are its principle subjects, the unions said in a joint statement.
Merci Patron is a Michael Moore-style documentary that follows the efforts of the Klurs, a couple who were laid off by an LVMH subsidiary, to contact Arnault and ask for help as they are threatened with the loss of their home.
Ruffin, who edits the left-wing magazine Fakir, says that it gives "injustice ... a name, a face, a voice".
He hailed the "courage" of the journalists who protested and claimed that reporters from Le Parisien and another LVMH-owned title, Les Echos, had earlier told his press attaché that they loved the film but would not be able to write about it.
Another journalist told him that his film "makes you want to become a Bolshevik" but that he couldn't cover it for fear of losing advertising revenue, he said.
Earlier in the week an invitation to Ruffin to appear on Europe 1 television, not owned by LVMH but by the Lagardère group, was cancelled at the last minute, although he was invited to another show after the incident became public.
He took advantage of the occasion to lay into Lagardère group boss, Arnaud Lagardère.
Ruffin also claims that a charity pulled out of financing the film because it had links with LVMH.
In a statement supporting Ruffin, the SNJ-CGT union denounced the "personal connections between billionaires proved by the successive censorship by [Vincent] Bolloré at Canal + [a TV channel] so that his 'friends' are not hurt", while the director declared that "the freedom of the press is theatened by the ownership of the means of production by these big capitalists who know each other and spend time together".
Nine media groups, several of them conglomerates with interests in industries stretching from fashion to armaments, control the majority of the French media, apart from public broadcasters like RFI.
Bernard Arnault, the world's 14th-richest person, is no stranger to spats with the press.
In 2012 he threatened to sue Libération newspaper for its headline "Clear off, rich loser!" referring to his application for Belgian nationality, which the paper interpreted as an effort to become a tax exile.
He dropped the case after the two sides reached an agreement.