Imagine Roger Nichols and Graham Johnson at a dinner party, discussing the composer about whom they have each published an entertaining and learned new biography: Francis Poulenc (1899-1963). Nichols, an eminent and prolific scholar of French music, would, on the evidence of his book, be an admirable and slightly frustrating guest, refusing to gossip. Johnson, I feel, would settle in for a good and not unsubtle conversation about Poulenc’s sex life, and perhaps would be persuaded, over coffee, to perform some of the music: a renowned accompanist, he has unparalleled practical knowledge of the terrain.

Nichols begins with a list of his subject’s contradictions: “between religious faith and doubt, between hetero- and homosexuality, between popularity and profundity, between tonality and modernity”. Any good biography of Poulenc, like the music itself, will make clear that none of these inclinations need be opposites. Poulenc was a composer who melded the incompatible. Famously described as a combination of “monk and ragamuffin”, he wrote music that the mind can mistrust but the heart will adore. He clung resolutely to tonality and melody in a century that had other ideas. His humour and light, his sheer loveliness, have led to suspicion.

But the more mischievous Poulenc becomes, the more he manages to be sincere. His music can provide a commentary on itself, the buttery melodies, even at their most passionate, spiked with rug-pulls, undercuts, little bubbles of flatulent woodwind. He can be “simply heavenly” in both a celestial and a Nancy Mitford sense. His mighty opera Dialogues des Carmélites is known for its numbing finale, in which 14 nuns are sent to the guillotine during the Reign of Terror, the noise of the descending blade slicing them from the music one by one. That Poulenc dares to venture so perilously close to sentimentality, even kitsch, at such a moment, can give the scene an astonishing power.

Poulenc’s life is rich terrain for a biographer, from his comfortable upbringing and brief time in the army, to his joining of the musical group eventually known as Les Six, and his loss and recovery of a powerful Catholicism. After making an unsuccessful marriage proposal to a beloved woman friend, he fathered illegitimately a child raised as his god-daughter, and took to roving the Paris streets by night in search of illicit sex with men. But Johnson’s and Nichols’s real concern is the music: both are convinced of its complexity, depth and importance. Nichols may be the more persuasive, simply because he tries less hard to persuade (Johnson uses “masterpiece” some 20 times, and “perfect” nearly 50). Focused so heavily on the compositions, neither could have avoided technical vocabulary and analysis, but neither uses notated music examples and, vitally, both have wit.

Nichols is more scholar than storyteller. He has occasional fun with the tangles of Poulenc’s liaisons, and there’s more than a whiff of Victoria Wood to the arrival of the last lover, “a 28-year-old junior executive at Citroën”. But Poulenc’s character and personal life all but disappear. His daughter is mentioned just thrice; his lover, Raymond Destouches, appears for the first time as an “ex”, discussion of the affair mainly omitted. Nichols’s most pleasing character is Paris, its cultural and political life forming a bright backdrop painted from decades of research, although he is not always adept at crowd control (31 individuals appear on page 19) and he assumes much foreknowledge, not least of the French language.

Johnson’s book is woven around Poulenc’s numerous songs, which Johnson argues “form a biography in themselves”. Readers may be sceptical of such an avowedly biographical reading of the work itself, and there will be admirers of Poulenc’s operas and instrumental music who won’t agree that the songs are the most personally revealing of his output: major choral pieces such as the Gloria and Stabat Mater, barely mentioned here, are surely a vital part of Poulenc’s peculiarly irreverent devotion. Structurally, the book is a bit of a jumble: there are chapter-length timelines; lists of works; lengthy and often brilliant analyses of the songs; translations of their texts; thematic essays; and interludial portraits of friends and colleagues. But Poulenc is there, alive on the page: hypochondriac, self-critical and self-centred, with a taste for fine tailoring and good food, and a capacity for bleakness and adoration. The translations (by Jeremy Sams) also make this a valuable compendium, not to say a triumph of copyright clearance.

Johnson writes with certainty, in his opening sentence: “Of Poulenc’s genius… there can now be little doubt.” Nichols waits until his conclusion: “In his best work Poulenc comes very close, at the least, to joining that small and illustrious band [of geniuses].” His slight hesitation is telling. It is very hard to catch Poulenc being a genius. He could somehow take a handful of almost brazenly familiar tropes and, unseen, nudge them from cliche into magic. This elusive tonal alchemy is part of his attraction: how can shallows have such depths, obviousness such subtlety, conventionality such subversiveness? The more Poulenc emulates other composers, the more he sounds like nobody other than himself. Perhaps it is simply that his reverence for them is worn right next to his heart, on his impeccably tailored sleeve.

Oliver Soden is the author of Michael Tippett: The Biography

• Poulenc: A Biography by Roger Nichols is published by Yale University Press (£25). To order a copy go to guardianbookshop.com. Free UK p&p over £15

• Poulenc: The Life in the Songs by Graham Johnson is published by WW Norton (£39). To order a copy go to guardianbookshop.com. Free UK p&p over £15