According to the magazines, Trierweiler had sought 20,000 to 25,000 euros for breach of privacy over the snaps taken when she and Hollande were holidaying in the Bregancon presidential retreat on a small island off the Mediterranean coast.
Judge Anne-Marie Sauteraud however said Trierweiler "could not ignore that by bathing in a two-piece swimsuit on the beach of the official presidential retreat, she risked being photographed".
French glossy VSD was fined 2,000 euros in September over the same photographs.
Closer in September created a storm by publishing photographs of Prince William's wife Catherine sunbathing topless. French legal authorities have since banned the magazine from any further distribution of the pictures.
A court also ordered the magazine to hand over the files with the images of the British royal couple, which the publication has done.
Disgraced ex-IMF chief Dominique Strauss-Kahn and a woman named as his new girlfriend are also seeking damages from Closer and VSD, for publishing "stolen photographs" of them together.
------------------------------------------------------------------------------------------