"I have received a letter from the lawyers of The Doors who are giving me 60 days to change the bar's posters, its name, the name of its cocktails and the website," Christophe Maillet, manager of the Lezard King bar, told AFP.
"The Doors did not want to be associated with a drinks bar," added Maillet, who opened the venue in September last year.
The bar's name is a tribute to the band's frontman Jim Morrison, who was known as the Lizard King after coining the term in a poem. It serves cocktails named after Doors songs such as "Soft Parade" and "Light My Fire".
"I thought I was doing a good thing, burnishing the image of The Doors," Maillet said. "I didn't ask permission but I suspected they would immediately refuse if I did."
He said he had told the US lawyers he would bend to their demand if they insisted.
Morrison died in Paris of a drug overdose in 1971 and is buried there in the Pere Lachaise cemetery.