There are elements of both realism and Gothic horror, but there is no actual supernatural event.
The Victorian novel Jane Eyre is both a romantic and a realist book because it has elements of both genres. The novel realistically tracks Jane’s difficult childhood and growth to a young woman, but it also contains strong gothic elements of darkness, madness, and violence.
First of all, the novel is realistic in how it depicts Jane’s childhood. Jane is an orphan who is sent to live with her terrible aunt, and then sent away to school. School is full of hypocrisy, and not much better than her aunt’s house. Jane learns pluck and determination. Her aunt poisons the schoolmasters’ minds against her, so they dislike and mistrust her from the beginning.
“Deceit is, indeed, a sad fault in a child,” said Mr. Brocklehurst; “it is akin to falsehood, and all liars will have their portion in the lake burning with fire and brimstone: she shall, however, be watched, Mrs. Reed; I will speak to Miss Temple and the teachers.” (ch 4, p. 26)
Jane is not a deceitful child. She is simply trying to survive. Reasonably, the only way Jane can survive is as a governess. The relationships she has with the household members are reasonable. For example, she cannot be in love with Mr. Rochester, even though he loves her, because of the differences in their classes.
He is not of your order: keep to your caste, and be too self-respecting to lavish the love of the whole heart, soul, and strength, where such a gift is not wanted and would be despised. (ch 17, p. 118)
In the end, Jane does mature enough to accept this, and she flees. Ironically, it is also her maturity that returns her to Mr. Rochester, because she realizes that she does love him, he really loves her, and they can be together.
The novel’s main Gothic elements are images of darkness and violence. For example, Jane is terrified of the Red Room.
Daylight began to forsake the red-room; it was past four o'clock, and the beclouded afternoon was tending to drear twilight. I heard the rain still beating continuously on the staircase window, and the wind howling in the grove behind the hall… (ch 2, p. 12)
The Gothic elements include the symbolic color of the room, red like blood, and the darkness, clouds, rain and howling wind. There is a prevalent motif of darkness. Later, the storms, mysterious sounds in the house, and the fire are all Gothic elements. The strongest Gothic element is Mr. Rochester’s “mad” wife, as craziness and violence are common in Gothic novels.
[The] lunatic sprang and grappled his throat viciously, and laid her teeth to his cheek: they struggled. She was a big woman, in stature almost equalling her husband, and corpulent besides: she showed virile force in the contest… (ch 26, p. 214)
The fire is one of the strongest Gothic touches, but there is a general harshness and dreariness to the landscape of the Moor that Victorian writers loved to take advantage of. Gothic novels often have a supernatural element, but everything in this story ends up having a rational explanation.