It always puzzles me when film-makers buy the rights to a book which they presumably consider to be a masterpiece and then change the story; not simply adapt the book for filming but significantly change the plot, the action and the motivations of the characters.
That is what has been done in this film, which is loosely based on Rosemary Sutcliff's book "The Eagle of the Ninth". Perhaps the fact that the film is entitled simply "The Eagle" is a confession that the screenplay has done violence to the book.
It is not as if the changes are improvements. Marcus and Esca set off in search of the lost Eagle of the Ninth Legion. Only when they are north of Hadrian's Wall does Esca (who is a Briton) say to Roman Marcus, "Let me do the talking." Did they really set off with so little forethought? No. In the book, Marcus goes north in the guise of an oculist, which gives him an entree to, and respect from, all the tribes they encounter. Marcus has no need to pretend to be Esca's slave. It is a much better scheme than the film's improvisation. Also in the book, Marcus gives Esca his freedom before they go north, so that they go on the quest as friends.
I suppose this is a good enough film but my advice is to read the book.