Irish filmmaker and songwriter John Carney has never been afraid of a little sincerity. In fact, he’s a champion of earnestness, making big, swoony feelings set to incredible music the core of his filmmaking since his 2007 breakout hit “Once,” which scored the Oscar for best original song for the achingly beautiful love song “Falling Slowly,” by Glen Hansard and Marketa Irglova. He wraps his homespun and heartfelt stories, which also include “Begin Again,” and “Sing Street,” in tunes that range from catchy to poignant, and his latest, “Flora and Son,” is no exception.

He’s also got a star with a remarkable rock ‘n’ roll pedigree in Eve Hewson, the daughter of U2 frontman Bono. She anchors the film as Flora, a young Dublin mother yearning for more. But Hewson’s famous father is of no import here, as she owns the screen with her mischievous charm, inhabiting Flora’s sharp wit and uninhibited nature, which is undergirded by a raw vulnerability. Hewson also has a gorgeous singing voice, but that might be afforded to her just by virtue of her Irish heritage.

When we meet Flora, she’s stampeding to the dance floor to lose herself in a thumping techno beat, and potentially in the arms of a stranger. Electronic dance music is her on-screen signature, and Carney charts her musical evolution alongside her personal journey over the course of “Flora and Son.”

Flora is young and beautiful, but she has a routine and responsibilities that supersede her her wild nights out — keeping her 14-year-old son Max (Orén Kinlan) out of trouble, tangling with her ex Ian (Jack Reynor), Max’s dad, and working as a mother’s helper. But like a lot of Carney characters, Flora is stuck. She dreams of something more, but she doesn’t know what, exactly. By a stroke of luck, and determination, she finds it in a garbage dumpster.

What she finds is a busted acoustic guitar that she thinks might keep Max out of trouble. When he expresses disinterest, it sits in the corner like a telltale heart, beckoning Flora to pick it up. She’s driven by her desire for purpose and passion, and also by spite, wanting to stick it to Ian, who enjoyed a modicum of success with his band years ago when they first met (“we shared a bill with Snow Patrol,” he brags). So she chugs some wine and signs up for online guitar lessons with a soulful SoCal bard named Jeff (Joseph Gordon-Levitt), who opines about songwriting with Topanga Canyon looming in the background.

In “Flora and Son,” Carney is interested in the way that music and songwriting can bridge vast distances, both geographical and emotional, which are themes he constantly returns to in his work, though they seem as fresh and exciting as ever. As Flora grows closer to Jeff, an escapist fantasy from her dreary Dublin life, Carney liberates him from the screen of her laptop. They strum and sing together in her kitchen and in the park, and she offers frank notes on his songs, the shared experience of making music allowing them to traverse oceans and continents.

In her real life, music becomes the thread that connects Flora to Max as well, as she discovers he’s making electronic beats. It becomes an activity that binds mother and son as they collaborate on songs and music videos, Flora hyping up the quiet, withdrawn Max to become the hip-hop superstar he dreams to be. Making music also provides neutral ground to find peace with Ian as well, as Flora reshapes her tiny dysfunctional family into a new iteration.

There’s an air of magical realism to Carney’s films, as fate and fantasy slip and slide together when chords thrum the air. It’s reflected in how he imagines Jeff and Flora in the same space together; it tickles the edges of Flora and Max’s collabs. But “Flora and Son” remains grounded in reality, and in Flora’s responsibility, her family, her son. Her purpose in life was of course in front of her all along, she just needed to find herself in the mix, too.

Carney’s insistence on sincere, guileless emotion in both songwriting and filmmaking (he and Scottish musician Gary Clark co-wrote the original songs) makes for intensely open-hearted works. But his script is typically Irish, imbued with playful jabs and crude humor, and Hewson’s forthright and foul-mouthed performance proves to be the perfect hit of sweet-and-sour acid to offset what could have been impossibly treacly. She’s a superstar in the making.

It’s almost unbelievable that Carney pulls off films like this, which could easily tip over into cheesy or maudlin territory. Instead, this winning yarn “Flora and Son” is an utterly irresistible emotional earworm.