In June 1950, the black American writer James Baldwin wrote a piece entitled "The Negro in Paris" for a journal called the Reporter. He had arrived in the French capital two years earlier, on a one-way ticket and with no intention of returning to the US (though the articles he filed home, especially those published in the Partisan Review, would soon make his name in the country of his birth).

Baldwin had been welcomed in Paris - at Jean-Paul Sartre's favoured café Les Deux Magots, to be precise - by the novelist Richard Wright, who had himself left America for Europe in 1946, a little over half a decade after the publication of his landmark novel Native Son, the tale of a wretched inhabitant of Chicago's "Black Belt" who goes to the electric chair for the murder of a white woman.

Baldwin and Wright would subsequently fall out when the former, in one of the articles that he sent back to the PR, criticised Native Son in the strongest terms for reproducing a debilitating and distinctively American "fantasy" of "Negro life". Because Wright saw novel writing as a form of "social struggle" - rather than a means of transmuting the motley of personal experience into art, as Baldwin regarded it - his protagonist, Bigger Thomas, lacks any "discernible relationship to himself", let alone other people. He is, instead, an entirely "mythic" creature - mythic because Wright abstains from any treatment of the complex reality of African-American life, with its shared traditions as well as its internal differences.

What Wright's portrayal of Bigger misses - because it is smothered by the character's inarticulate rage - is any sense of the endless "paradoxical adjustments" that are required of the black American. The essays that Baldwin wrote in Paris (later collected in an anthology entitled, in deference to his former mentor, Notes of a Native Son) attempt to register the complexities he found so catastrophically lacking in Wright's novel.

In his Parisian exile, Baldwin came to see that he was "a kind of bastard of the west". The monuments of European high culture - Shakespeare, Bach, Rembrandt - were not really his; yet, he wrote, there was "no other heritage which I could possibly hope to use. I had certainly been unfitted for the jungle or the tribe." The predicament wasn't peculiar to Baldwin, however. As a new exhibition at Tate Liverpool shows, it was the situation in which many of the most important artists and writers of the black diaspora found themselves from the early 1900s onwards. "Afro Modern: Journeys through the Black Atlantic" takes its cue from Paul Gilroy's groundbreaking work of cultural history The Black Atlantic: Modernity and Double Consciousness, which argues for the importance of that black diaspora to 20th-century art and literature.

“The Negro in Paris" offers a particularly vivid account of one African American's fraught identification with western modernity. He distinguishes there the situation of "Negro entertainers" (jazz musicians and singers) in Paris from that of their "non-performing coloured countrymen", most of them former servicemen studying abroad thanks to the provisions of the GI Bill. The latter tended not to enjoy the "comradeship" of other black Americans, but lived in a kind of unsplendid isolation. "The American Negro in Paris," Baldwin writes, "is very nearly the invisible man."

On the rare occasions that he is noticed, it is by Frenchmen who see America - and all Americans, black or white - through the prism of its own self-aggrandising myth-making. Thousands of miles from home, the "non-performing" black American "finds himself involved . . . in the same old battle: the battle for his own identity". And it is a battle that is made more intense still by his encounters with black Africans from France's colonies, who, for all their bitterness at their condition, at least have an unambiguous relationship with their homeland. The black American, whose bitterness is more likely to be "turned against himself", feels an alienation from his African counterpart so complete as to induce in him the recognition that he is a "hybrid" - not a "physical hybrid merely [but] in every aspect of his living".

“Someone, someday," Baldwin would write later, "should do a study in depth of the role of the American Negro in the mind and life of Europe." Although he didn't live to see it, his wish came true in 1993, when the The Black Atlantic was published. Gilroy treats the European exile of writers such as Baldwin and Wright, as well as the transatlantic journeys of the father of black nationalism and pan-Africanism, W E B Du Bois, as the crucible of a notion of black identity that renounces the temptations of ethnic separatism and nationalism, and sometimes even the idea of "race" itself.

The subtitle of The Black Atlantic emphasises the influence exercised on Gilroy by Du Bois's theory, developed in his magnum opus, The Souls of Black Folk (1903), of "double consciousness" - the "unreconciled striving" inside the breast of every black American that Baldwin had felt so keenly by the banks of the Seine. In Gilroy's account, Du Bois's work is a complex, sometimes incoherent, skein of racial particularism, black nationalism and something at once richer and more unresolved. And one of the vehicles for this latter mode of black self-assertion was the work of art, now understood not as a kind of compensation for the African American's "internal exile from modernity", but rather as a privileged form of his engagement with it.

This is borne out by one of the rooms in the Tate Liverpool exhibition, whose curators, Tanya Barson and Peter Gorschlüter, have used the theoretical framework of Gilroy's book as a prism through which to consider an extra­ordinary parade of 80 years of art from the black diaspora (not to mention work by non-black giants of modernism such as Picasso and Brancusi, who themselves explored the "transcultural space" that Gilroy would later scrutinise in his book). Under the banner of "Black Atlantic Avant-Gardes", visitors encounter the work of the painter Aaron Douglas, one of the prime movers of the Harlem Renaissance of the 1920s and 1930s and a protégé of Du Bois.

In the murals that Douglas painted for Fisk University in Nashville, as well as in the gorgeous, delicate relief prints he made for Du Bois's journal The Crisis, forms derived from African art collide with a sensibility informed by European modernism. The Guyanese-born painter Frank Bowling, who contributes a red, gold and green slab of abstract expressionism to the show, once said, perhaps with half an eye on Du Bois, that the "black soul, if there is such a thing, belongs in modernism".

This remark is as cogent a summary of Gilroy's outlook as one could wish for - not least because it tells us something new about modernism, as well as about black identity. It resonates, too, with the work of the "post-black artists" displayed in the final room of the exhibition - for instance, with Glen Ligon's Gold Nobody Knew Me #1, on which is reproduced a line of Richard Pryor's with which, you suspect, Baldwin would have sympathised: "I went to Africa. I went to the motherland to find my roots! Right? Seven million black people! Not one of those motherfuckers knew me."

“Afro Modern: Journeys through the Black Atlantic" is at Tate Liverpool until 25 April (tate.org.uk/liverpool)