The photos in the celebrity-focused magazine Voici are the first to be published of the couple together since news of their secret liaison broke earlier this year.
Voici editor-in-chief Marion Alombert said the pictures of Hollande and Gayet inside the walled and guarded Elysee presidential residence in the centre of Paris were taken in October.
They are seen sitting on the terrace of one of the palace suites, and appear to have been taken with a very long zoom lens.
Hollande and Gayet's relationship was broken by a rival French magazine, Closer, in January.
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It triggered a very public break-up between Hollande and his long-term partner Valerie Trierweiler, who retaliated with a tell-all book that savaged the president's personal and political reputation.
The latest snaps have raised questions about security measures at the palace. Alombert confirmed that Hollande is "someone who sometimes has holes in his security".
She told French TV station BFM that the three published photos of the couple were "not taken from inside" the palace "nor by a drone".
She did not, however, reveal how the pictures were taken.
The Elysee refused to comment on the lastest photos when contacted by AFP.
Trierweiler's book, "Merci pour ce moment" (Thank you for this moment), published in early September, portrayed Hollande as a champagne socialist who actually "despises the poor". An English-language translation of the book is to be released next week.
Although some critics have perceived a rather unhinged tone to the book, its assertions has done little to improve the image of Hollande, already the least popular president in French history for his failure to revive the country's flatlining economy.
She will no doubt face questions about the latest photos, whose provenance looks set to remain a mystery.
"It is part of the trust that photographers put in us when they offer these kinds of photos," said Voici's Alombert.