In a joint statement, Industrial Renewal Minister Arnaud Montebourg and the junior minister for the digital economy, Fleur Pellerin, said Facebook managers had been summoned before France's CNIL data watchdog to explain the rumours.
"Clear and transparent explanations must be given without delay," they said in the statement.
Facebook on Monday said it had investigated complaints from members and denied the reports of private messages being made public.
"A small number of users raised concerns after what they mistakenly believed to be private messages appeared on their Timeline," the California-based social network said in an email response to an AFP inquiry.
"Our engineers investigated these reports and found that the messages were older wall posts that had always been visible on the users' profile pages."
Concerns that private Facebook messages from 2007, 2008, or 2009 were being posted for public viewing spread wildly on message service Twitter Monday after a story first appeared in the free French daily Metro.
"Facebook management is unable to give us any explanation of what happened," Pellerin said on i-Tele television. "Today complete confusion reigns and Facebook's explanations are not very convincing."
"If there is ever any real certainty that private messages were made public and that there was a breach of confidentiality... I would advise people to file a complaint. This is unacceptable," she said.