The singer-songwriter is the wife of former President Nicolas Sarkozy. In a song entitled, "The Penguin," Bruni uses a French nickname for someone who is seen as all dressed up but still lacking grace and manners.
According to The Hollywood Reporter:
"She mocks [President Hollande's] “sovereign air.” “He takes on the airs of a king, but I know the penguin does not have the manners of a lord,” read the lyrics. Bruni was widely said to feel slighted when Hollande skipped the customary walk with the departing couple as they exited Elysee Palace, instead staying in the garden to pose for photos. “Hey penguin, you look all alone in your garden,” she sings. “If one day you cross my path, I’ll teach you to kiss my hand.”
In a blitz of interviews with French media to promote her album, Bruni also said a formal investigation of her husband opened last week for allegedly exploiting the mental frailty of 90-year-old L'Oreal heiress Liliane Bettencourt was causing her great pain.
"It's impossible to imagine that this man could have abused the frailty of a lady the age of his mother... It's unthinkable," Bruni told RTL radio in a shaky voice.
Sarkozy, who retreated from front-line politics after losing his re-election bid last May, rejects accusations that he took advantage of Bettencourt, France's richest woman, in 2007 to raise funds for his first election campaign. He wrote on Facebook this week that the probe against him was "unfair and unfounded".
The case could scupper any political comeback for Sarkozy, whose remains a popular figure for center-right voters and has said he would consider running for president again in 2017.
His lawyer, Thierry Herzog, has said he would seek to have the case thrown out on grounds that the investigation conducted by judge Jean-Michel Gentil was biased against Sarkozy.
A former model, Bruni played a restrained role as first lady while Sarkozy was in power but has since returned to the media spotlight, performing last week at the ECHO Music Awards in Berlin.
Bruni's 2008 marriage to Sarkozy after a whirlwind courtship irritated many French people who felt the high-profile romance blurred the lines between the president's private and public lives.
Asked if she was tempted to fight back publicly against the accusations and "show her claws", Bruni said: "Yes, I want to but I don't dare. It is difficult for me to talk about this, it's painful for my family."
(Editing by Catherine Bremer and Toby Chopra)