The spider and the fly Frollo sees serve as philosophical symbols of fate and nature. Frollo feels that he is both spider and fly in his relationship with Esmeralda, and she is the same with him. His sexual obsession with her make him like the fly, prey to sin. However, his predatory feelings towards her also make her his inevitable victim as well.

These spider and fly symbols also relate to Frollo's ideas about fate and free will: just as the spider always traps and devours the fly, so too will Esmeralda be victimized by his lust and so too will he be destroyed by his own lust for her. Frollo feels there is no escaping this doomed game. He (and indeed, many other characters in the novel) have a very deterministic view of life. They do not seem to believe they have any free will to fight their desires and actions.

There are, of course, many symbols in Hugo's novels, but two of the most important are the Notre Dame Cathedral and Esmeralda's red baby shoes.

The cathedral serves as a symbol of France, specifically, it represents the possibility of a return to France's former glory. 

Esmeralda's red shoes are a symbol of innocence and purity.  Recall that Esmeralda was kidnapped by gypsies when she was a child.  Her mother managed to save one of her baby's red shoes.  Years later, young Esmeralda meets with a gypsy who has the mate to her baby shoe.  The gypsy tells Esmeralda that as long as she remains virtuous, that one day, she and her mother will be reunited.