Half-way through Soundtrack to a Coup D’Etat, John Coltrane and Duke Ellington’s soulful version of In a Sentimental Mood is interrupted. Suddenly, we see and hear Malcolm X giving a speech at New York’s Harlem Square in 1960. It’s like being shaken from a delicious reverie and thrown into the ice bath of reality.

“You’ll never get Mississippi straightened out,” Malcolm X snaps at the Harlem crowds, “until you start realising the connection with the Congo.” The curious connection between Black Americans’ fight for civil rights and the second-largest country in Africa is the subject of Johan Grimonprez’s documentary.

Early on, his film quotes political philosopher Frantz Fanon: “Africa is shaped like a gun, and the Congo is its trigger.” Described thus, the Congo doesn’t sound a peaceful place. “It isn’t,” says Grimonprez. “The Congo was long raped and plundered for its raw materials. It still is. You wouldn’t have your Teslas or your iPhones without raw material from the Congo.

“And I don’t mean rape just metaphorically. If you made a map of the east Congo showing where the mining is and the statistics of how many women are raped, it’s a one-on-one correlation.”

His film juxtaposes the racist lynchings and de facto apartheid of southern American states such as Mississippi in the 1960s with the contemporary assassination of Patrice Lumumba, Congo’s first democratically elected, Black African post-colonial prime minister. His film reveals how Lumumba was toppled in a military coup aided – either actively or through docile complaisance – by the CIA, MI6, 20,000 supposed peacekeepers deployed by UN Secretary-General Dag Hammarskjöld, freebooting mercenaries like “Mad Mike” Hoare and, finally, Belgium, whose secret service worked with white colonists desperate to retain their African assets.

“I thought it was time to dig into my own country’s past,” says the Belgian director from his New York hotel room. “When I grew up, it was all around me. But I didn’t really know about the nitty gritty. This film is about the nitty gritty.”

Belgium, Grimonprez says, is younger than the US, but, thanks to its ruthless colonial exploitation of Congo for its mineral riches, its exploitation of Black people mirrored slave-era America. “If the United States was behaving like a teenager, then we were behaving like a toddler.” Only in 2002, the film reveals, did Belgium formally apologise for the role its partisans played in Lumumba’s torture and murder. His killing made Lumumba a pan-African icon and hero across the Atlantic to African Americans (Malcolm X named his daughter Lumumba).

Grimonprez doesn’t only indict Belgium. The 62-year-old director has walk-on roles from not just some of the greatest jazz musicians ever (Max Roach, Abbey Lincoln, Coltrane, Art Blakey, Quincy Jones – the list goes on), but shady characters such as British spy Daphne Park, our woman in Stanleyville. It includes chilling archive footage of this MI6 agent who looks and sounds like Miss Marple but was one of the brains behind the coup that did for Lumumba. Her policy of surreptitiously fomenting dissent between Congolese politicians, the better to undermine the first prime minister of a free, post-colonial Congo, clearly worked. Without Park’s interference and that of her CIA counterparts, the downfall of Lumumba might not have been so precipitate.

But why did the west dabble in the Congo? This is where Grimonprez’s film is especially rewarding. It takes us back 64 years, to a time when Black African nations were shaking off the colonial yoke and simultaneously figured as proxies in the cold war. Lumumba had the misfortune to be regarded by the US state department as a dangerous red. The film quotes US President Dwight Eisenhower’s reported hope that “Lumumba would fall into a river full of crocodiles”.

“Lumumba was no communist,” says Grimonprez when I put this to him. “He was a Black nationalist like many African leaders at the time.” Footage suggests he was also an immensely charismatic man, who spoke eloquent truth to power. We see him amid the pomp and circumstance of Congo’s Independence Day ceremony on 30 June 1960, when he told dignitaries, including the Belgian king, of his pride in leading the push for Congolese liberation: “[I]t was a noble and just struggle, and indispensable to put an end to the humiliating slavery which was imposed upon us by force.” King Baudouin was reportedly livid at Lumumba’s ungrateful tone.

Six months later, after being ousted from office by western-backed army officer Joseph-Désiré Mobutu, Lumumba was kidnapped and tortured, then finally shot dead by Belgians under orders from the Katangan government. While some think it speculative that the CIA was involved, Grimonprez has no doubts: “Eisenhower got his wish.” His body was dug from its shallow grave, dissolved with sulphuric acid and the bones ground up.

Others in Lumumba’s circle were a little more fortunate. Lumumba’s chief of protocol, Andrée Blouin, smeared as an African Mata Hari by the western media, survived two assassination attempts and fled to Paris. Her children were not allowed to go with her: they remained in the Congo as bargaining chips to buy her silence.

As well as acts of unspeakable cruelty, the film also introduces us to murderous gizmos that would have made 007’s M envious. A CIA-agent nicknamed “Joe from Paris” travelled to the Congo armed with toothpaste concealing poison to be used in a so-called heart attack pistol to assassinate Lumumba. He was, Grimonprez argues, under orders from the Dulles brothers – John, who was President Eisenhower’s secretary of state, and CIA director Allen. These were the two Americans subject to Winston Churchill’s withering assessment, quoted in the film: “Dull, duller, Dulles.”

As for jazz’s role in Lumumba’s downfall, Grimonpez’s film reveals how the great trumpeter Louis “Satchmo” Armstrong became embroiled in the Dulles brothers’ machinations as a cultural ambassador to the Congo. It was as fatuous a policy as sending Taylor Swift or Beyoncé to bring about peace in the Middle East. No matter: jazz was used as soft power to spread American values to counter the Soviet threat, and as handmaiden to the CIA’s destabilisation of elected governments. Says Grimonprez: “Dave Brubeck was sent to Syria, Armstrong went to Katanga [the short-lived state established inside the Congo in 1960] to give it legitimacy.”

Grimonprez doesn’t portray Satchmo as CIA stooge, though. “He wasn’t a passive instrument. He refused to play in apartheid South Africa and when he found out what the state department were plotting in Katanga and that he was being used to gather information for the CIA, he was furious. He threatened to leave America and go live in Ghana.”

The film includes footage of a concert Armstrong gave in Accra before Ghana’s first post-independence leader Kwame Nkrumah. We see Nkrumah in the audience quietly crying as Armstrong sings (What Did I Do to Be So) Black and Blue:

“My only sin is in my skin / What did I do to be so black and blue? / I’m white inside but, that don’t help my case / This life can’t hide what is in my face”

“He changed the words when he sang that to Nkrumah,” Grimonprez tells me, “Instead of ‘I’m white inside’, he sang ‘I’m right inside’.”

Yet despite his musical insights, Grimonprez is no jazz buff. I supposed that he realised that Lumumba’s downfall coincided with such a golden age of jazz that he just flicked through his record collection to select his movie’s soundtrack. This was the era, after all, of Coltrane’s Giant Steps, Eric Dolphy’s Out to Lunch, Miles Davis’s Kind of Blue and Ornette Coleman’s The Shape of Jazz to Come.

“It was the other way round. I knew the politics but not the music. I found out about that,” he says. Could he have made this documentary without jazz? “No. The music is integral to the film. If the politics is all about dividing and conquering, it’s the music that brings people together. And even if it’s a scream of anger, it can also be an energy that opts for a change in this world.”

When we hear Nina Simone exquisitely perform Wild Is the Wind in the film, it’s not hard to hear precisely that. Her motif of the derangement of love takes on other resonances. This wild wind may carry not just radioactive dust from a looming nuclear armageddon, but something more hopeful: the “winds of change” evoked by Harold Macmillan in 1960.

By that phrase, the British prime minister meant the end of white colonial rule from Delhi to Accra (if not in apartheid Cape Town, where he made that speech). Soundtrack to a Coup d’Etat opens a new perspective on the cold war in which the west is afraid not of reds under the bed, but Black Africans running their own contras. True, one reason the CIA was involved in the Congolese domestic politics was out of fear that the Kremlin might get its hands on Congo’s Uranium-235 stocks after the country became independent from Belgium. But the US and its allies, Grimonprez convincingly suggests, were battling another foe. “They were terrified of the United States of Africa proposed by Kwame Nkrumah. Stanleyville [today Kisangani, capital of Tshopo Province] would have been the capital of that United States, by the way. The west was never going to allow that to happen.”

Congo was the focus for that new front in the cold war because of fears the material wealth of this long-exploited colony would fall into the wrong hands.

For a few moments in 1960, though, the Congo might have been different. “With your kiss my life begins,” sings Simone on Wild Is the Wind, and, as she sings, Black Africa’s life and Congolese self-rule was beginning. Another song, Indépendence Cha Cha by the king of Congolese rumba Joseph Kabasele, quoted in the film, captures that short-lived pan-Africanist joy:

“Indépendance, cha-cha, tozoui e / Oh! Kimpwanza cha-cha, tubakidi”

“Independence we’ve won it / Oh! Independence we’ve achieved it)

But they hadn’t. “The Congo was too valuable an asset for it to be allowed to be truly independent,” says Grimonprez. Every war in the 20th century was fought with minerals from the Congo. The rights to its uranium have been signed away in perpetuity.” Novelist In Koli Jean Bofane, author of Congo Inc, points out it in the film that without Congolese raw materials, the US would not have been able to bomb Hiroshima and Nagasaki, nor fire bullets in Vietnam.

In the film, there is a heart-catching sequence when we hear John Coltrane blowing a few peerless bars from My Favourite Things. The music cuts off abruptly. We see tanks rolling through the Congo as the military coup subverts democracy. We cut back to Coltrane, his face contorted in rapturous agony as he blows his now-unheard solo. Grimonprez thereby shows us the tragic disconnect between Congolese aspiration and reality and that paradox, inexpressible pain. It’s a pain described in the film by In Koli Jean Bofane: “Nobody sees the tears of a fish.” Soundtrack to a Coup d’Etat, most remarkably, finds a way of making us see and feel what we miss in our everyday experience – that pain, those tears, that tragedy.

• Soundtrack to a Coup D’Etat is released in the UK on 15 November

• This article was amended on 14 November 2024. An earlier version described Kisangani as the capital of the Democratic Republic of the Congo. It is in fact the capital of Tshopo Province.