When life throws you a conceit, you run with it. No, really. A conceit is an unintuitive extended metaphor that requires some explanation before it convinces us that it actually works.
So while a story about spiders and flies may sound at first sound like something that should be narrated by David Attenborough, in this novel we're asked to see it as a metaphor for the fate of our characters. None other than Frollo introduces us to this idea:
"This is a symbol for the whole affair. She is young, she flies around. She is merry, she seeks the open air, the spring sunshine, liberty. Oh, yes! But she is stopped at the fatal window; she is caught in the toils of the spider, the hideous spider! Poor dancing girl! Poor predestinated fly! Be quiet, Master Jacques! It is Fate!" (VII.V.29)
Now we understand how fate is working in this novel—or, at least, how Frollo thinks fate is working. Fate is inevitable, and it is nefarious. Like a spider, Frollo can't help but catch and devour the fly (Esmeralda), who in her turn can't help but fly around and eventually get caught in the spider's (Frollo's) web.
But, as Frollo goes on to say, the caught-by-Fate metaphor applies to him as well:
"Alas, Claude! You are the spider. Claude, you are the fly too! You did seek science, the light, the sunshine; you only wanted to reach the open air, the broad daylight of eternal truth. But while darting toward the dazzling window, which opens into the other world, a world of brightness, intelligence, and science, blind fly, silly doctor, you did not perceive that subtle spider's web, spread by Fate between the light and you" (VII.V.29)
Esmeralda might be "caught" by Frollo in a more literal sense, but Frollo is also "caught" in his own lust for Esmeralda. The point is, neither of them is going to make it out the window.
The spider-and-fly image comes up a few times in the novel: take a look at when Esmeralda is being tortured (VIII.II.19) and when Esmeralda is hanged (XI.II.17). These are moments when the idea of being "caught"—and of Fate having run its course—is really palpable.