Actually, when I saw the first Avatar, I thought that it was much closer to the "Treasure of Silver Lake" ("Der Schatz im Silbersee") by Karl May, combined with many scenes from the earlier novels of Karl May.

Many characters of that series of Karl May novels have a direct mapping, e.g.:

Old Shatterhand => Jake Sully

Winnetou => Neytiri (gender swapped)

tamed mustang => tamed flying dragon

and many others.