The lyrics of "The Penguin" were released on Friday and immediately interpreted as an attack on the man who succeeded her husband, Nicolas Sarkozy, as France's leader.
The former supermodel sings: "He takes on the airs of a king/but I know the penguin/doesn't have the manners of a lord./Hey penguin!/If one day you cross my path again/I will teach you, penguin/I will teach you to kiss my hand."
French media saw the lyrics as a reference to Hollande's frosty treatment of his outgoing predecessor on the day when he took over as president, notably declining to accompany Sarkozy to the car that carried him away from the presidential Elysée palace.
In French, describing someone as a penguin implies they are both clumsy and a little ridiculous in the manner of a clown or a buffoon.
"The Penguin" is one of the tracks on "Little French Songs", Bruni's fourth album, which is due to be released on April 1st.
It also includes a song, "Chez Keith et Anita" ('At Keith and Anita's place'), in which Bruni, a former girlfriend of Mick Jagger, depicts the drug-fuelled lifestyle of Rolling Stones guitarist Keith Richards and his longtime girlfriend Anita Pallenberg.
The new album is Bruni's first since 2008's "Comme Si De Rien N'Etait" ('Simply'). Her musical career was put on hold while Sarkozy was in office.