There are traces of romantic influence throughout. The title is one; to call something or someone "a simple heart" evokes the stylized simplicity of childhood, as one might encounter in fairy tales. Likewise, the opening line is as simplified as the opening "once upon a time." The story closes with a more formally Romantic touch; her soul goes to heaven, and the description is lushly vivid. So, the phrasing and perspective are romantic.
The realism is found in the critique of the Catholic church, and the explicit discussion of labor and suffering of the servant.