The Musée d'Orsay is one of the biggest tourist draws in Paris and home to some of 19th Century French art's most famous nudes.
But when French literature student Jeanne visited wearing a low-cut dress on a hot day this week, she says she was barred from entering.
Museum staff told her "rules are rules" and she was eventually allowed in when she put on her jacket, she explains.
Her story has gone viral on social media and the museum has apologised.
She posted a picture of herself sitting in a restaurant four hours before going to the museum with a friend, describing how first one official then another stared at her breasts but did not say which rule she was contravening.
Temperatures reached 26C on Tuesday, and Jeanne, an art-loving literature student, told of her desire to mark the end of a hot afternoon at the Musée d'Orsay. "It was far from my mind that my cleavage would be the subject of any disagreement," she says.
Although her friend had a cropped top that showed her navel, Jeanne says attention was fixed on her breasts even before she had had a chance to show her ticket. "Oh no, that's not going to be possible, that's not allowed, that is not acceptable," she quotes a ticket agent as saying.
A guard then arrived citing museum rules, she says. "At no time does anyone say my cleavage is a problem, they're manifestly staring at my breasts, referring to them as 'that'."
Initially she refused to put on her jacket. "I don't want to put on my jacket as I feel beaten, compelled, I'm ashamed. I feel everyone's looking at my breasts. All I am is my breasts; all I am is a woman they are sexualising."
When Jeanne's Twitter post went viral the museum responded, saying they had become aware of an "incident" involving a visitor.
"We deeply regret it and apologise to the person involved, with whom we are getting in touch," it said.
She told the BBC she was satisfied that the museum "contacted me personally by phone and has been very understanding, providing me with a very sincere apology". But she felt the museum's public response on Twitter "fails to recognise the sexist and discriminatory nature of the event".
She was not bitter about what happened and loved art too much to resist going back, she said.
What is not clear is which rules the museum meant. The Libération newspaper points to a couple of rules referring to "decent dress" and a ban on clothing "likely to disturb the peace" but it believes the museum clearly realised they were not relevant in this case.
The talk at the museum is of "overzealous" officials, according to Le Parisien website.
After all, this is one of Paris's favourite tourist destinations, home to world-renowned nudes such as Gustave Courbet's graphic Origin of the World, Edouard Manet's Olympia and Auguste Renoir's Grand nu.