First things first: The Eddy, a new Netflix drama about a Paris jazz club, directed by La La Land’s Damien Chazelle and written by Jack Thorne, is not, repeat not, a musical. “It’s a show about musicians,” Thorne says. “There is music in it, but the music is music that the band have written and that they’re performing. It’s not a musical.”

Instead, what Thorne, Chazelle, his producer, Alan Poul, and the composer Glen Ballard have created is a love song to music, musicians and modern-day Paris. “It started when Alan approached me around the time I was premiering Whiplash at Sundance,” Chazelle says, referring to his 2014 breakout hit about a young jazz drummer and his perfectionist tutor. “Glen had gone to Alan with an idea about doing a show set principally in a jazz club in contemporary Paris.”

Ballard had already written half of the songs. He had even been road-testing a band he was calling the Eddy in Los Angeles clubs. The idea was that the show would follow the lives of a ragbag of local expats as they struggle to keep the club afloat, including the club owner, Elliot (André Holland), his estranged daughter, Julie (Amandla Stenberg), his co-owner, Farid (Tahar Rahim), and the individual members of the house band.

Chazelle has an American mother and a French father; he grew up living between Paris and America. He was also a jazz drummer in high school, so, after Whiplash and La La Land, The Eddy — the music, the club and the city — was right in his wheelhouse. He was particularly inspired, he says, by classic documentaries such as Jazz on a Summer’s Day, a concert film set at the 1958 Newport jazz festival, in Rhode Island, and Straight, No Chaser, a 1988 documentary about Thelonious Monk.

The idea was that the show would follow the lives of a ragbag of local expats as they struggle to keep the club afloat.

“These were documentaries about music performance where the cameras were still carving out what exactly they could do and what the relationship to the performers could be,” he says. “We knew we were telling a fictional story, but the performance and the music had to have an authentically documentary element within that.”

On the set last year you could see what Chazelle and his team were trying to capture. They had closed off a street in the 20th arrondissement to film the Eddy band on foot. Handheld cameras filmed several takes up and down the cafe-lined street as the players riffed and improvised. The band leader, Randy Kerber, was on accordion, Lada Obradovic was tapping out rhythms, Ludovic Louis trilled on trumpet, Jowee Omicil was on saxophone and Damian Nueva Cortes played bass.

Proper jazzers will recognise those names: the band is something of a jazz supergroup. Kerber has played keyboards on everything from Titanic to the Harry Potter films — he tutored Ryan Gosling for La La Land. Ballard, who wrote the songs, worked with Michael Jackson and Quincy Jones, and produced the Alanis Morissette album Jagged Little Pill. Louis is a longtime Ballard collaborator who plays in Lenny Kravitz’s band … and so on. The music feels vital because the performers are musicians.

“We knew that the whole thing would rise or fall based on capturing performance,” Chazelle says. “Basically that dictated the style of the whole show to us. These would need to be real musicians, not actors faking being musicians.”

Chazelle was particularly inspired, he says, by classic documentaries such as Jazz on a Summer’s Day, a concert film set at the 1958 Newport jazz festival, in Rhode Island, and Straight, No Chaser.

That meant that when it came to the lead role of the band’s singer, Chazelle had only one name in mind: Joanna Kulig. With her sleepy eyes and smoky voice, Kulig was flawless in Pawel Pawlikowski’s Cold War. There she played a singer in a doomed love affair, and she did it so well that last year she was in Los Angeles for the Cold War Oscar campaign. It was there her agent told her Chazelle had asked to meet her.

“I was super-happy, because I saw La La Land seven times!” she says, speaking in Berlin last month. “I used to sing those songs between takes on Cold War to relax. Damien loved Cold War — that was why this happened.”

Chazelle and Ballard asked Kulig to tape a couple of songs for The Eddy. She preferred to sing live — “It’s the energy that’s so important” — so she went to Ballard’s Hollywood studio and performed. Three hours later they called to say she had the part. Kulig was so good that the role was changed from an American called Kelly to a Polish woman called Maja.

Seven days later Kulig gave birth to her first child. One of the most remarkable things about her already remarkable performance in The Eddy is that she was breast-pumping milk between takes, for scootering over to her baby’s nanny in a nearby Paris apartment. “We were shooting in Paris, working in French, English and Arabic with Damien and three other directors. I’d been living in LA for six months for the Oscar campaign before we started shooting, then I had six months in Paris singing all these songs, and with a new baby. It was, like, ‘Oh my God.’ One year was like three years.”

Looking back, she says that playing a jazz singer — at times, being a jazz singer — was the role she has always wanted to play. “I grew up in Poland wanting to be a jazz musician, but in Poland we don’t have a lot of secondary music schools for jazz singers.”

At 19 Kulig tried and failed to get into the Katowice Academy of Music, the only music school in Poland that teaches jazz singing, with just two places available a year. So she enrolled on a course in music and drama at the National Academy of Theatre Arts in Krakow.

“The entrance exam was the most strange for me,” she says. “They said, sing something — easy for me. Play on the piano? OK. But shout, cry? They wanted to check all my emotions, and that felt strange. But slowly, slowly, I noticed that if you work like an actor, sometimes it’s easier to interpret songs, and vice versa — music helps you in your feelings for acting.”

Two years into her course Kulig was picked by Grzegorz Pacek for his documentary-style film Wednesday, Thursday Morning, and when Pawlikowski gave her a role as a singer in his 2013 movie Ida, Kulig had found her director and he his muse.

“Pavel created for me the character Zula in Cold War, which connected a lot of things. It takes in my childhood a little bit [Zula starts out as a folk singer; Kulig’s father was a folk poet]. Pavel knew I had a classical musical education. And at the same time he knew I had something interesting, a very husky voice. He created the perfect part for me. I sing, I act, I dance. That is perfect.”

The Eddy is available on Netflix