As we start getting more information on the new Narnia adaptation, I see people worrying it won't stay true to C. S. Lewis's vision. Now, as a white British man writing in the 1950s, if Lewis imagined POC characters in his books, it was as
nobles and royals, leaders and officers, heroes and legends, friends and love interests and protagonists.
Caspian X is a main character in Prince Caspian and The Voyage of the Dawn Treader, and the title character of Prince Caspian. He begins the story as a prince, and ends it taking his rightful place as "lawful King under [Peter] in Narnia both by [Peter's] gift and by the laws of the Telmarines" (Prince Caspian, chapter 13: The High King in Command). Caspian leads a war, overthrows a tyrant, and sails on a journey across the Eastern Ocean to save the lords who had been tricked into being lost at sea because they would have supported Caspian. Brave and loyal, he earns not one, but two, epithets through his actions: "Caspian the Seafarer" (The Silver Chair, chapter 12: The Queen of Underland"; the title is also used several times in The Last Battle) and "Caspian the Navigator" (The Silver Chair, chapter 16: The Healing of Harms").
He is also a Telmarine. The Great Lion himself explains what this means.
"You, Sir Caspian," said Aslan, "might have known that you could be no true King of Narnia unless, like the Kings of old, you were a son of Adam and came from the world of Adam's sons. And so you are. Many years ago in that world, in a deep sea of that world which is called the South Sea, a shipload of pirates were driven by storm on an island. And there they did as pirates would: killed the natives and took the native women for wives, and made palm wine, and drank and were drunk, and lay in the shade of the palm trees, and woke up and quarrelled, and sometimes killed one another. And in one of these frays six were put to flight by the rest and fled with their women into the centre of the island and up a mountain, and went, as they thought, into a cave to hide. But it was one of the magical places of that world, one of the chinks or chasms between that world and this. There were many chinks or chasms between worlds in old times, but they have grown rarer. This was one of the last: I do not say the last. And so they fell, or rose, or blundered, or dropped right through, and found themselves in this world, in the Land of Telmar which was then unpeopled." (Prince Caspian, chapter 15: Aslan Makes a Door in the Air)
Nowadays, we would say Caspian is Polynesian.
The Silver Chair features "the King's son of Narnia, Rilian, the only child of Caspian, Tenth of that name" (The Silver Chair, chapter 12: The Queen of Underland"). One of the protagonists of The Last Battle is Tirian, whose "great-grandfather's great-grandfather" was Rilian. Like Caspian, they are heroes and kings, and Telmarines of Polynesian descent. Caspian and Rilian had such golden reigns that Tirian remembers them, and specifics of their stories, hundreds of years later (The Last Battle, chapter 9: What Happened That Night).
Calormen is a large kingdom to the south of Narnia. While its origins are never given, both the text and the original illustrations (by Pauline Baynes, with input and approval from Lewis), clearly show it is based on the Middle East; its citizens are described as dark-skinned. Tarkheena is a Calormene title, the feminine version of Tarkaan, meaning "great lord", while Tisroc is the Calormene equivalent of king or emperor (The Horse and His Boy, chapter 1, How Shasta Set Out On His Travels).
One of the protagonists of The Horse and His Boy is "Aravis Tarkheena ... the only daughter of Kidrash Tarkaan, the son of Rishti Tarkaan, the son of Kidrash Tarkaan, the son of Ilsombreh Tisroc, the son of Ardeeb Tisroc who was descended in a right line from the god Tash. [Her] father is lord of the province of Calavar and is one who has the right of standing on his feet in his shoes before the face of the Tisroc himself (may he live for ever)" (The Horse and His Boy, chapter 3: At the Gates of Tashbaan). In the book, Aravis is brave, quick-thinking, and independent, with a strong character arc based around pride and generosity without ever losing her fierce spirit; afterwards, she marries another protagonist, Prince Cor, "and after King Lune's death they made a good King and Queen of Archenland and Ram the Great, the most famous of all the kings of Archenland, was their son" (The Horse and His Boy, chapter 15: Rabadash the Ridiculous).
Lasaraleen Tarkheena plays a supporting role in The Horse and His Boy. Aravis's friend, she is earnest, friendly, and loyal, risking herself to help Aravis even when she can't see the appeal in Aravis's chosen life. (The Horse and His Boy, chapter 7: Aravis in Tashbaan; chapter 9: Across the Desert)
Emeth is a minor character in The Last Battle. A Calormene officer, he is brave, pious, and honorable; he is also courteous, well-spoken, and learned, quoting "the poets" (The Last Battle, chapter 10: Who Will Go Into the Stable; chapter 14: Night Falls on Narnia; chapter 15: Further Up and Further In).
As for other characters, there is very little in the books indicating they are of one ethnicity or another. Cor is explicitly stated to be "white and fair", because he has to be; it is a plot point (The Horse and His Boy, chapter 1: How Shasta Set Out on His Travels). Jadis is repeatedly described as very pale as a way to indicate how strange and otherworldly she looks (The Magician's Nephew, chapter 13: An Unexpected Meeting; The Lion, the Witch and the Wardrobe, chapter 3: Edmund and the Wardrobe). Many characters have minimal or no physical description. Lewis's writing style leaves a great deal to imagination; a clear image of all the characters simply cannot be formed from textual evidence alone.
What can be said is that a truly book-accurate adaptation of Narnia, as envisioned by C. S. Lewis, will have a diverse cast.