Gayet, 44, pressed charges against the magazine after the grainy images of the couple on a terrace inside Hollande's official residence were published in 2014 under the tagline: "Since the start of their affair we have never seen them together."
The images sparked concerns over security surrounding Hollande, 61, and after investigations showed the pictures were taken from within his residence, five members of his private security detail were transferred to other posts.
A lawyer for the magazine told AFP they planned to appeal. If the sentence is upheld Voici will have to publish a legal statement on its front page.
Gayet's lawyer, Jean Ennochi, said there was no "legitimate interest" in publishing the pictures.
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"I hope this conviction will put a stop to this kind of publication of photos taken in private places. It is a crime," he said.
In October, Voici and another celebrity magazine VSD were ordered to pay 1,500 euros to Gayet and members of her family after picturing them with Hollande at one of his official country residences.
Trierweiler, a journalist, published a bestselling tell-all memoir of their relationship and break-up, portraying the president as a cold-hearted egotist and champagne socialist, who was contemptuous of the "toothless" poor.
Trierweiler says in the book she tried to commit suicide in the presidential bedroom with an overdose of sleeping pills after news of the affair broke.
Hollande has remained mum on his relationship with Gayet ever since, refusing to confirm or deny their relationship.