I used to own a copy of the novelization. In fact I read it before I saw the movie, so when I did finally see the movie, the differences surprised me.
In general, it is very faithful to the film, however, except for a few small differences in dialogue, and of course the song lyrics being rewritten into dialogue and abridged.
These are the main differences I remember:
*The opening chapter, titled “The Puppeteer’s Prologue,” frames the whole story as having happened in the past and being told by Clopin in his puppet show - unlike in the film, where Clopin’s puppet show takes place before the main plot begins and only tells Quasimodo’s backstory. Clopin explains that he knows the story because he saw much of it with his own eyes and heard of it with his own ears, and before he starts to tell it, after saying that it’s a tale of a man and a monster, he says that maybe when it's finished, the children will be able to tell him who is the monster and who is the man.
*Frollo doesn’t kick Quasimodo’s mother onto the cathedral steps. Instead she just loses her footing while struggling with Frollo over the baby and accidentally falls.
*There's no drawn-out chase scene between Esmeralda and the guards after she stands up to Frollo. Esmeralda just makes herself "disappear" in a puff of powder-smoke and then slips away through the crowd. She doesn't pretend to cry and then activate the powder-smoke with a fake nose-blow either – she just tosses the powder into the air.
*Esmeralda and Phoebus don’t fight in the cathedral: she wields the candelabra and warns him “Don’t come any closer!” but doesn’t actually try to hit him with it, or grab his sword and threaten him with it for that matter, and then he goes straight to introducing himself.
*At the end of the scene corresponding to "God Help the Outcasts," there's no man who yells at Quasimodo to go away. Esmeralda just spots Quasi watching her, and when their eyes meet, he runs away out of shyness.
*Esmeralda explicitly tells Quasimodo that the woven necklace will show him the way to the Court of Miracles, rather than just saying a cryptic rhyme about it that he figures out later.
*During the scene corresponding to “Hellfire,” Frollo thinks to himself that maybe God has destined him to lead Esmeralda to righteousness. I might have liked some dialogue like this in the finished film, because it would more clearly explain Frollo’s motives: to either change his “sinful” lust into something pure and holy, by making Esmeralda his wife and converting her to his form of Christianity, or else to get rid of the temptation by killing her.
*When Frollo says to Phoebus "But you were trained to follow orders," Phoebus retorts "Not the orders of a madman!" Obviously, the filmmakers decided that less was more by having him just silently douse the torch.
*When Esmeralda brings the wounded Phoebus into the bell tower, Quasimodo brings water for her to clean his wound, rather than her cleaning it with wine.
*Quasimodo’s reluctance to go with Phoebus to find Esmeralda and warn her about Frollo’s plans comes across as slightly more spiteful than it does in the finished film, per se. “Esmeralda didn’t love him after all. She he loved Phoebus. Why should he help her?” Likewise, when Esmeralda is about to be executed, and Laverne tells him “These chains aren’t what’s holding you back,” she also adds “I think you’re still jealous.” Personally, I don’t like this – while I admit, we can interpret the finished film’s Quasi as almost wanting to turn his back on Esmeralda because he’s bitter that she doesn’t love him, I’d rather think his initial refusals to act are based in fear and self-doubt, with just an undertone in the first case of “She doesn’t need me when she has Phoebus."
*When Quasimodo and Phoebus arrive at the cemetery, Quasi is described as supporting Phoebus, who is still weak from his wound. I might have liked to see that instead of his improbably quick healing in the finished film.
*In the Court of Miracles, Quasimodo is the one who announces that Frollo is attacking at dawn with a thousand men, rather than Phoebus. Then when Phoebus tells Esmeralda "Don't thank me, thank Quasimodo," he then adds "He's the real hero." Esmeralda responds by hugging Quasi and saying "I think I know that better than anyone." Then Phoebus announces to all the Romani, not just Esmeralda, that without Quasi, he never would have found his way there.
*Esmeralda doesn’t spit in Frollo’s face when he says “Choose me or the fire”: she just says nothing. Frollo's speech afterwards is also different: there's no line about sending "this unholy demon back where she belongs."
*During the climactic battle, there’s some dialogue between Quasimodo and the gargoyles that explains the vat of molten lead in the bell tower and what it’s used for (to repair cracked bells), as Quasimodo realizes that they can rain it down on the soldiers. Obviously this dialogue would have slowed down the action in the movie, but it might have been nice to provide an explanation – maybe people would stop calling the lead “lava” then.
*Quasimodo doesn’t sob over Esmeralda’s body when he thinks she’s dead, or have any dialogue with Frollo before the latter tries to stab him - he just exclaims “Oh no!” when he can’t wake Esmeralda, then suddenly notices the shadow of Frollo raising the dagger behind him.
*Phoebus has some dialogue with Quasimodo after he saves him from falling to his death, first joking a little and then expressing sincere gratitude that he was in the right place at the right time.
*The little girl in the final scene doesn’t hug Quasimodo, but just gently touches his face, then leads him down into the crowd. This is also true in other movie storybooks, so I suspect the hug was a later addition to the script, to ensure that the audience would realize that the girl was showing Quasi warmth and gratitude.