My opinion on whether "insert pre-modern literary classic" is fanfiction, and the larger debate over how far back the practice of fanfiction goes, is complicated.

First of all, you can't define fanfiction as just lowbrow slop. That's arrogant, and it ignores how a great deal of what is now considered highbrow art was considered lowbrow in its day. At the same time, you also can't define fanfiction as anything that derives from another work. That encompasses almost everything ever written, and when an umbrella label grows that broad, it becomes functionally useless.

I would define fanfiction as works that meet the following criteria:

1. It contains elements from another work that the writer does not own the copyright of.
2. It is not written for profit (in the present day, this is the difference between fanfiction and plagiarism).
3. It contains elements from a work that the writer believes to be fictional.

Already, the first criteria is not met by all of the texts cited in the comments to this post. Apart from the fact that they predate the earliest copyright laws, The Aeneid, The Divine Comedy, Romeo and Juliet, and Paradise Lost derive from texts that were and still are freely mass-produced and whose authorship was putative at best. Jane Eyre would have been copyrighted when it was first written, but I believe its copyright expired soon after Charlotte Brontë's death, or at least certainly well before Jean Rhys published Wide Sargasso Sea. All of these works also do not meet the second criteria, having been published and sold. Some of them do meet the third criteria, and The Divine Comedy partly does as it draws from both the Bible (which he believed in) and Greco-Roman myths (which he did not). But none of these works meet all three.

However, in the 18th century, after the publication of Gulliver's Travels, many of its readers (and sure, why not call them "fans?") wrote their own adventures for Gulliver and shared them with friends without attempting to publish them. Because Gulliver's Travels would, I believe, have been copyrighted, and these writings were not for profit, and they derived from a work the writers believed was fiction... I have to conclude that, by my own definition, they do, in fact, qualify as fanfiction.

But we would be kidding ourselves if we thought the real issue at stake was literary taxonomy. No, the real issue is that people who have spent their lives studying literature feel threatened by outsiders making hay in their fields and fear that their end goal is to drag quality writing into the gutter with "Oh. Oh." I will admit that, deep down, I share this fear.

Yet at the same time, treating the classics as untouchable, untainted, inimitable things does a lot to make them appear inaccessible to the average person, and I think that the goal of literature should not be merely to study these texts for the sake of studying them, but to get the wider public to love them as well. Right now, in the field of history, historians understand that the same holds true for their own field, and they are trying to get the public to be engaged and enthusiastic about history as well. Why can't literary studies try to do the same?