Born to Coppola and her husband, Thomas Mars, frontman of the French indie pop band Phoenix, Romy released the debut songs on Wednesday (22 May). The tracks were produced by bedroom pop artist Claud.
Both "Stuck Up" and "From a Distance" feature Romy singing in a deadpan, confessional style over pared-back instrumentation, including shuffling percussion and buoyant acoustic guitar strums.
She was previously brought to the internet's attention thanks to a viral TikTok in 2023.
In the clip, Romy made pasta with a vodka sauce while regaling viewers with a tale about how she was grounded for trying to charter a helicopter from New York to Maryland using her father's credit card so she could hang out with her friend.
She claimed to not know the difference between garlic and onions, and introduced viewers to her babysitter's boyfriend "because my parents are never home so these are my replacement parents".
She also posed with her father's Grammy and said she started a TikTok against her parents' wishes: "They don't want me to be a nepotism kid but TikTok's not gonna make me famous."
The now-deleted TikTok racked up millions of views and likes, with many fans declaring Romy "the greatest nepo baby".
Romy's mother, Sofia Coppola, met her father Thomas Mars while he was working on music for her film The Virgin Suicides. They have since collaborated on the music for all of Coppola's ensuing films, including her critically acclaimed 2023 biopic Priscilla.
She told The Guardian in a 2017 interview that she had endeavoured to keep her two daughters, Romy and Cosima, out of the spotlight. "I don't want them to ever feel jaded and I've never seen the value of taking kids to premieres or things like that," she said.
Speaking to The Hollywood Reporter about the viral clip, Coppola acknowledged that Romy posting the video was a way for her daughter to be "rebellious".
"We were raised to be so private, and social media is so the opposite of how I grew up," Coppola said in August last year. "So it was the best way for her to be rebellious."
While acknowledging her daughter was "funny" and she had received lots of compliments about her daughter's video editing skills and comedic talent, Coppola added: "People discussing my parenting publicly is not what I would've hoped for."
Romy made her red carpet debut last week with her grandfather, Francis Ford Coppola, at the Cannes Film Festival premiere of his controversial sci-fi drama Megalopolis.
The legendary director's self-funded dystopian film had its world premiere at the festival on Thursday 16 May, after taking decades to make at a cost of around $120m (£96m).
The film stars Adam Driver as Cesar Catilina, an architect-scientist who wants to better a fictional version of New York City called New Rome. Megalopolis also features Aubrey Plaza, Shia LaBeouf, Laurence Fishburne, Dustin Hoffman and Nathalie Emmanuel.
Coppola condemned the criticism around the film, calling it "unpardonable" to "attack a movie because it doesn't play by Hollywood's current rules, by quoting unnamed sources who probably weren't at the screening and may not exist".
As for critics who have labelled the film a "passion project", he retorted: "I've never made a film that wasn't a passion project.
"Who wants to see a film that someone made without passion, or even a meal that the chef had not prepared passionately? As for the genre they want to force my film into, sci-fi: no, Megalopolis is a fable of future history."
