71-year-old François Néri is accused of publishing false and defamatory information on his blog, Le Systémicien, in July.
The rumours concerned allegations that Aubry, who is currently fighting to win the Socialist party nomination to stand in next year's presidential elections, is "homosexual" and an "alcoholic." The blog also accused her husband, the lawyer Jean-Louis Brochen, of being a secret Islamist radical.
"One has the right to be militant and to be in disagreement with Martin Aubry," said the couple's lawyer, Yves Baudelot. "But one does not have the right to attack Martine Aubry and spread odious and false statements without any verification."
Néri's lawyer, Renaud Bettcher, replied that the accusations had been "said before and said again" and that it was "the one who said them last who gets slapped."
Bettcher went on to ask why none of the other publications had been the object of a lawsuit from Aubry and her husband, including mass publication magazines such as Le Nouvel Observateur.
Aubry's lawyer said that the couple had decided "enough was enough" and that the blog in question had the "advantage" of "capturing all the rumours that were circulating on the net."
A verdict will be given on October 17th.