I haven't even played Fiasco yet, and it's probably not going to turn out to be a favorite game since I don't seem to like the genre much; but I keep trying to think of places where it could be used. I think that's a natural outgrowth of my effort to understand what the genre actually is. (For instance, I still haven't gotten anyone to talk about whether it could be used to run something like The Out-Of-Towners.)
So I was thinking about whether you could use it to tell a story set in the same world as Jane Austen's books, but it would necessarily be a different story. So far as anyone I talked to can think of, there are no major works set in that period which actually tell a fiasco-like story. Protagonists often face terrible adversity but in some way, they triumph over it. Antagonists often come to messy ends, but as a result of comeuppance for their acts. There are grim things in stories, but they don't have the same character as in fiasco movies. You might even say that fiasco movies are in part a reaction against a standard paradigm of storytelling that was thrown into sharp focus during the period in question.
Thus, in playing Fiasco in that setting, or just writing a fiasco story in it, you would be fighting against the grain of all the tropes that the setting usually brings, and you would have to watch what you were doing very carefully. It would be quite a challenge. But I think if you could pull it off, the contrast and incongruity would be powerful, and force a new look at a familiar time period and setting. It could be very incredible, but it'd be very easy to get wrong.
The time period is rife with fiasco-like outcomes, though. Consider how badly ruined you are in that time if your reputation is sullied, and how hard it is to recover -- a story element Austen plays with extensively. Consider how mind-numbingly awful debtor's prison is (even if that speaks more of Victorian than Regency periods in terms of appearing in the fiction of each time, though they certainly fit into either). Consider how terrible the medicine of the time is, so even a minor injury can be crippling for life. The seemingly spotless ethics of Jane Austen's characters barely concealed a deep fascination with forbidden perversions of all sorts even amongst the upper classes. The disparities between the classes, and the way people of different races are treated, provides tons of fodder for the kind of motivations that would drive a fiasco story. And while many fiasco stories are firmly rooted in the criminal and working class worlds, with even the bigwigs little more than the biggest dung-beetle in a dung-heap, I think a lot could be done with tossing one or two upper-class folks into the mix, either slumming, or just drawn into the schemes by whatever desperate ploys one side or the other have used.
Since I am doubtful I'm even going to do "vanilla" Fiasco very well, I'm certainly not the person to explore these ideas farther. I am not even that familiar with the Regency period, and have never read any Jane Austen, beyond the snippets one can't help but absorbing through exposure to pop culture and some notable Austen fans in one's circle. I probably would have little fun playing in a Regency Fiasco. But I hope someone can use the idea.