At the end of the first paragraph, the narrator swoons.
If you are like my students, they do not immediately know what "swoon" means. It means to faint, to lose consciousness, to pass out, and/or to black out.
The reader does not know for sure that the narrator...
has lost consciousness until the reader reads the first sentence of the second paragraph. At the start of that paragraph, the narrator flat out announces that he "had swooned."
Swooning does carry a slightly different connotation than a simple passing out. When a person swoons, it is often because of an emotional overload. Having the narrator swoon at the end of the first paragraph makes perfect sense, because the narrator has just been sentenced to death. From the moment that his death sentence is pronounced, the narrator starts to lose touch with reality. He admits that he no longer hears specific words.
The sentence -- the dread sentence of death -- was the last of distinct accentuation which reached my ears. After that, the sound of the inquisitorial voices seemed merged in one dreamy indeterminate hum.
By the end of the paragraph, the narrator is hallucinating and wishing for death.
And then there stole into my fancy, like a rich musical note, the thought of what sweet rest there must be in the grave.
His mind simply can't handle everything that is going on, so he swoons.