Keith Richards, left, and Brian Jones in The Stones and Brian Jones (Getty Images/Magnolia Pictures)

Fortuitously, Nick Broomfield’s latest documentary comes on the heels of Hackney Diamonds, the Rolling Stones’ most well-received and commercially successful album in decades. But Broomfield is more interested in vintage Stones history. His coruscating film chronicles the short life and tragic demise of the Stones’ founding member, guitarist Brian Jones. He recruited Mick Jagger, Keith Richards, Bill Wyman, and Charlie Watts to form what would become, as an ending title card reminds us, the world’s greatest rock ’n’ roll band.

Jones, who loved the blues, wanted the Stones to become a platform for his passion. Indeed, the Stones’ first hit on the British charts, in 1964, was “Little Red Rooster,” originally popularized by Howlin’ Wolf a few years earlier. Yet Jones started losing the battle for the direction the Stones would take due to the blossoming songwriting partnership of Jagger and Richards. Once “(I Can’t Get No) Satisfaction” (a song Jones wasn’t particularly enamored of) became a huge hit in 1965, Jones’s influence began waning, and the clichéd temptations of the rock ’n’ roll lifestyle—mainly, sex, and drugs—took over.

Jones’s musical contributions to the group became so infrequent that, by the time he was let go from the band in June 1969, he didn’t seem to be that surprised. A few weeks later (July 3, to be exact), Jones was found dead in his swimming pool, one of the first members of the so-called 27 Club, musicians who died at age 27. (Jimi Hendrix, Jim Morrison, and Janis Joplin would soon join him.)

Broomfield outlines a story that’s familiar to music fans in his usual engaging way, painting a vivid picture of Swinging ’60s London as the backdrop for the Stones’ success and eventual demise of their founding member. He uses vintage interviews with Jones’s father, friends, former girlfriends, and musical colleagues as voice-overs along with rare footage and photos—like a rock’n’roll Ken Burns—and includes a rare image of a teenage Jones playing in the school band. But his conservative parents didn’t understand their long-haired, jazz-and-blues-loving son, and kicked him out of their house. (There’s a quite poignant moment late in the film when a letter from Jones’s dad is read, in which Mr. Jones laments his treatment of a son he didn’t understand.)

There’s a glimpse into Jones’s private life—he fathered no fewer than five children with five different women. Broomfield features some of them—many still sound positively enamored of Brian, even decades later—notwithstanding that in every instance he would quickly move on to someone else. Former Stones bassist Bill Wyman is also a willing participant in Broomfield’s sympathetic but non-hagiographic portrait. Credited as a consultant, Wyman appears on camera, touchingly reminiscing about a good friend and bandmate he still misses some 55 years later.

Broomfield also hears from two others whom Jones knew personally or professionally, and their insights are priceless. French actress Zouzou (best known as the lead in Eric Rohmer’s 1972 Chloe in the Afternoon) enthusiastically discusses her brief dalliance with Jones in the mid–’60s and how drugs were affecting his musicmaking. Filmmaker Volker Schlöndorff, who directed Jones’s then-girlfriend Anita Pallenberg—who would soon leave Jones for bandmate Keith Richards—in a 1967 film, Degree of Murder, bemusedly remembers seeing how Jones and Pallenberg’s volatile relationship was ignited by their drug taking and endless fighting.

That Brian Jones is now a footnote in the storied history of the Rolling Stones makes it even more imperative to watch Nick Broomfield’s film, which brings laser-sharp focus to Jones’s initial importance and, sadly, the human cost of his demons.