The reason the Battlefield One features a black soldier is because one of the preorder bonuses is the Harlem Hellfighters Pack. The Harlem Hellfighters was the nickname for the 369th Infantry Regiment, an all black US army unit which served with distinction while connected to the French Army during 1918. It was also the first African American unit to see combat and two African Americans, Henry Johnson and Needham Roberts, were the first US soldiers to receive the Croix de Guerre, a French decoration for distinguishing acts of heroism during combat. The 369th also holds the unfortunate distinction of holding the record for the longest time serving at the front with some 191 days of active service.

While the number of black soldiers who served during the First World War was quite small compared to the vast numbers of white soldiers, there was still a considerable number that fought during the war. The majority of these were colonial soldiers recruited largely from France's African colonies such as Algeria and Senegal (tragically, these colonial troops, along with the Canadians, were among the first Allied forces to experience the horrors of chemical warfare during the Second Battle of Ypres). The French were quite open to using black soldiers and the African American men that served alongside the French found them quite friendly and welcoming compared to their fellow white US servicemen (the US Army went so far as to publish a pamphlet intended to inform French civilians of "the alleged inferior nature and supposed rapist tendencies of African Americans."

Throughout the war, African men fought for all sides all over Africa as the French and British attempted to seize German colonial holdings such as German South-West Africa (now Namibia) and the Germans attempted to prevent this while making their own attempts as colonial expansion. If this piques your curiosity, I strongly suggest you read up on Paul Emil von Lettow-Vorbeck, the German commander who, for four years, repeatedly outmaneuvered and outsmarted the British, French and Portuguese forces that attempted to bring him to heel. His achievements are quite incredible seeing as he only had a force of about 3,000 German soldiers and officers and about 11,000 African soldiers from German colonies.

Sources:

The First World War by John Keegan

1914 1918: The History of the First World War by David Stevenson

American National Biography Online: Henry Johnson

/u/TheWellSpokenMan nailed it in his response. Hopefully my response will just be as useful. Farwell's book is definitely worth reading, and unlike some others that were published at the same time, does not hold back with being critical of Lettow-Vorbeck. Charles Miller's Battle for the Bundu romanticized Lettow-Vorbeck a fair bit for his use of guerrilla tactics, a point that is also often brought up whenever he is mentioned. Another element that is also romanticized about Lettow-Vorbeck is his relationship with his African soldiers. Based off his own writings, it seems as if Lettow-Vorbeck had a rather paternalistic outlook on them. While he did respect them as soldiers, he felt as if the colonization of East Africa and the introduction of German practices helped to "civilize" them. Similarly, Edwin P. Hoyt's book Guerrilla: Colonel von Lettow-Vorbeck and Germany's East African Empire praises German colonization, making the absurd claim that:

 

In Africa, however, the Germans left a mark that the British could never eradicate. As the blacks came to social and political maturity, they realized that the German colonization had been the most reasonable of all, and the mark of the Schutztruppe, an equality never felt before in Africa, was burned deep into the souls of the askaris, the carriers, and all the people they knew. The British did not learn between two wars about racism, and at the end of World War II they were surprised to find out that one after the other, the colonies rejected them. So much for the lessons of the past.

 

Lettow-Vorbeck's own account of the German East Africa campaign can be read in My Reminiscences of East Africa. Published after the war, 1920 I believe, Lettow-Vorbeck recounts his actions and feelings about the war and relationship with his African troops. He does admit early on that what he is writing may not entirely be accurate since he is remembering it.

 

There are several newer works that discuss World War I in Africa, with emphasis on the African soldiers. Both Edward Paice's Tip and Run: The Untold Tragedy of the Great War in Africa and Hew Strachan's The First World War in Africa are a good place to start. Michelle Moyd's Violent Intermediaries: African Soldiers, Conquest, and Everyday Colonialism in German East Africa and Timothy Stapleton's No Insignificant Part: The Rhodesia Native Regiment and the East Africa Campaign of the First World War are denser and more academic works, but also explore the involvement of colonial African soldiers in World War I.

 

Edit: Forgot the citation for Hoyt: Edwin P. Hoyt, Guerilla: Colonel Von Lettow-Vorbeck and Germany's East African Empire (New York, NY: Macmillan Publishing Co., 1981), 203.