What happens in Canto V of Dante's Inferno?

Canto V
In Circle Two, Dante meets the former lovers Paolo and Francesca. Their crime had been lust, and putting their carnal love and desire before their love and obedience to God. Appropriately, these two lovers are forever buffeted by strong winds, just as in life they were blown to extremes by their passion.
Francesca is allowed to pause long enough to explain her neverending misery to the poet:

"There is no greater sorrow
Than to be mindful of the happy time
In misery, and that thy Teacher knows.
But, if to recognise the earliest root
Of love in us thou hast so great desire,
I will do even as he who weeps and speaks.
One day we reading were for our delight
Of Launcelot, how Love did him enthral.
Alone we were and without any fear.
Full many a time our eyes together drew
That reading, and drove the colour from our faces;
But one point only was it that o'ercame us.
When as we read of the much-longed-for smile
Being by such a noble lover kissed,
This one, who ne'er from me shall be divided,
Kissed me upon the mouth all palpitating.
Galeotto was the book and he who wrote it.
That day no farther did we read therein."

As Francesca tells her story, her former lover, Paolo, is blown close enough to overhear. He is impaled by emotional pain, and Dante, recognizing his own weakness in regard to Beatrice, swoons:

And all the while one spirit uttered this,
The other one did weep so, that, for pity,
I swooned away as if I had been dying,
And fell, even as a dead body falls.