The weekly French magazine Closer published a seven-page article titled "Francois Hollande and Julie Gayet -- the president's secret love," Friday on its website, detailing the alleged affair between the president and the 44-year-old actress, Radio France Internationale reported.
"Around New Year's Day a helmeted head of state joined the actress at her apartment, where he is in the habit of spending the night," Closer wrote on its website.
Hollande called the article an "invasion of privacy," to which he, "like every other citizen, has a right," adding he was considering legal action.
Members of Hollande's Socialist party lashed out.
Prime Minister Jean-Marc Ayrault said Hollande is "perfectly right" to demand "respect for his private life."
"This is a totally private matter," Bruno Le roux, the Socialist leader in the National Assembly, told France Info radio. "Politics isn't conducted in the gutter press."
Opposition leaders also condemned the allegations made by Closer.
Far-right leader Marine Le Pen said as long as "it doesn't cost the taxpayer a centime ... everyone should have the right to a private life."