Prime Minister Edouard Philippe hailed the "madness that kept him company and never betrayed him" in a tweet that paid tribute to his talents as a poet and performer after the news of Higelin's death broke on Friday.
Paris mayor Anne Hidalgo, whose election campaign Higelin supported, expressed condolences to his wife, Aziza, and children, Arthur, Kên and Izia.
Rail worker father
Born in a village near Paris during World War II, Higelin was encouraged in his musical and theatrical interests by his father, Paul, a rail worker who played the piano.
Having left school at 14, he started his career in the theatre, where he was deeply impressed by jazzman Sidney Bechet, by then a French resident, when playing a small role in a musical Nouvelle Orléans (New Orleans).
In the 1960s he took drama courses, winning the François Périer prize.
But he was also obliged to do military service in Germany and Algeria, where he performed for officers and met musician Areski Belkacem, with whom he went on to cut his first two records.
Back in France he started performing with singer Brigitte Fontaine and the pair became known for their anarchic performances and left-wing politics.
By the end of the 60s, Higelin was performing with cutting-edge artists like the Art Ensemble of Chicago and strongly committed to left-wing politics, publicly supporting the May 68 strikes and protests and snubbing mainstream media outlets.
His political commitment led him to perform on Paris's Place de la République when France's first Socialist president, François Mitterrand, was elected amid left-wing euphoria.
He also gave concerts in support of undocumented immigrants and supported the homeless campaign, Droit au Logement (Right to Housing).
In the 1970s Higelin travelled and withdrew to communes in the south of France, while still managing to record his first solo album, Jacques Crabouif Higelin.
Rock, Youssou N'Dour, Mory Kanté
Musically he progressed from the café-concert-style to rock in the 1970s under the influence, notably, of David Bowie.
His stage appearances became more and more ambitious, sometimes leading critics to say he had overreached himself and accuse him of a tendency to kitsch while they praised his charisma and his poetic talents.
Higelin was fascinated by African music, touring Zaire (now Democratic Republic of Congo) and Senegal in the 1980s and bringing African musicians like Youssou N'Dour and Mory Kanté to France to perform with him.
In 2000 he toured the US in duo with Mahut, leading the New York Times to comment on his "radical politics" and say "his music offers a continent of charm".
Higelin's three children all followed him into performance - the oldest, Arthur H, is now a well-known singer, his son Kên is a director and his daughter, Izia, is an actress.
He had experienced health problems since 2010, leading to concerts being cancelled and hospitalisations.
His family announced his death on 6 April 2018.
Jacques Higelin, a life in dates
- 18 October 1940: Born in Brou-sur-Chantereine to Paul Higelin, a railworker originally from Alsace, and Renée, née Bourdouxhe, a Belgian;
- 1954: Leaves school, auditions for producer Jacques Canetti, who refuses to employ him because he is a minor but tells him to come back in 10 years;
- 1959: Plays in Henri Fabiani's film Le Bonheur est pour Demain (Happiness, that's for tomorrow);
- 1963: Plays in Yves Robert's film Bébert et l'Omnibus;
- 1965: Records his first albums with Brigitte Fontaine;
- 1968: Supports May 68 protests and becomes popular among students, refusing to talk to mainstream media;
- 1970: Plays in "happening-concerts" and improvises with avant-garde groups like jazz musicians the Art Ensemble of Chicago and rockers the Pretty Things;
- 1971: Performs the communist anthem the Internationale for the centenary of the Paris commune, records his first solo album, Jacques Crabouif Higelin;
- 1973: Booed when he appears playing just an accordeon as thesupport act for soul group Sly and the Family Stone at the Paris Olympia;
- 1974: Records rock album BBH 75;
- 1979: Records two complementary albums Champagne pour Tout le Monde (Champagne for everybody) and Caviar pour les Autres (Caviar for the rest), partly recorded in New Orleans;
- 1981: Gives a concert with the group Téléphone at Paris's Place de la République to celebrate the election of Socialist president François Mitterrand;
- 1982: Standing on a lorry packed with musical instruments, leads a procession across Paris at the city's second Fête de la musique;
- 1985: Records album Aï, brings Senegalese singer Youssou N'Dour and Guinean Mory Kanté to Paris to perform with him;
- 1987: Publishes his letters to Irène Popouche when he was doing his military service under the title Love Letters of a 20-year-old soldier;
- 1988: Records Tombé du Ciel, which sells 350,000 copies;
- 1997: Records 22nd album Paradis Païen (Pagan Paradise), gives a concert for undocumented migrants along with artists including Brigitte Fontaine and Algerian Cheb Mami, presented by RFI's Claudy Siar;
- 2005: Records album of songs by Charles Trénet;
- 2013: Records Beau Repaire;
- 2016: Records last album Higelin 75, publishes book of poetry Flâner entre les Intervalles (Strolling between the Intervals);
- 2015: Publishes book of autobiographical interviews, Je vis pas ma Vie, Je la Chante (I don't live my life, I sing it);
- 6 April 2018: Dies in Paris at the age of 77.