It is difficult to classify Jane Austen's works into one literary movement because she reacted against major literary movements of her time and thus created a style all her own. While it is difficult to classify her novels under Realism, we can certainly say that all aspects of her novels are realistic.
Austen began writing in the late 1790s, the same time in which Romanticism was developing, and along with Romantic literature came Gothic literature. Romanticism was a protestation against the Enlightenment, which placed emphasis on logic and reason. In contrast, Romanticism placed emphasis on emotions, especially on the emotions of the individual. Gothic literature used horror and death to paint mankind in a fallen state while also capturing ideals of Romantic literature. In many of her letters, we find Jane Austen protesting against the actions, emotions, and story lines found in both Romantic and Gothic literature. Plus, her novels Sense and Sensibility and Northanger Abbey parody Gothic literature and Romantic ideals. While parodying such literary works, she also strove to create characters, circumstances, and story lines that were realistic.
The Realism literary movement began developing in the mid-1800s as a reaction against Romanticism, just as Austen reacted against Romanticism. In contrast to Romanticism, Realism authors strove to capture life the way it truly was. Authors strove to be objective and not make any value judgements about life, which is the way in which Austen's novels diverge from Realism. Austen uses her realistic novels to moralize about humanity, class, and society.
Austen's creation of realistic characters, settings, situations, and story lines can be seen all throughout her works. Looking at Pride and Prejudice as an example, we see that, while Longbourn is fictional, it exists in England's real county of Hertfordshire. In addition, the characters in Austen's Bennet family can exist as real people: There certainly are men like Mr. Bennet who marry women for their beauty and soon fall out of love with such women because the women are too ignorant and self-serving; there truly can be a family consisting of five sisters; there certainly can be women like Elizabeth who are attractive, witty, and intelligent but think a bit too well of themselves; and there certainly are vain, dangerous flirts like Lydia, etc. The characters also participate in realistic activities fitting of Jane Austen's own social class, the landed gentry, such as attend balls, travel to London, and take summer trips. In short, Austen strives to capture life and society the way it truly was among her own social class, and, in doing so, she moralizes about the actions of members of her own class.