Appearance versus inner worth
Hugo sets up a world that punishes ugliness and rewards beauty, then shows how wrong that system is. Quasimodo is the most loyal and loving character in the book. Phoebus is the most admired and the most worthless. The gap between how characters look and who they actually are drives almost every tragedy.
Obsession as destruction
Frollo's desire for Esmeralda does not lead him to protect her. It leads him to destroy her. Hugo shows that obsession dressed up as love is still a form of violence, and that religious repression does not eliminate desire but makes it more dangerous.
Institutional cruelty
The Church, the courts, and the monarchy all fail the vulnerable characters. Esmeralda is tortured into a false confession. Quasimodo is flogged for a crime Frollo ordered. The systems that should deliver justice consistently protect the powerful and punish the powerless.
Sanctuary and its limits
Notre-Dame offers Esmeralda legal sanctuary, but that protection is fragile and conditional. Frollo can still reach her. The king can override it. Hugo uses the cathedral's sanctuary to show that even the strongest institutions cannot protect people when those in power decide to ignore the rules.
The clash between the medieval world and modernity
Frollo fears the printing press because he knows it will make the cathedral, and everything it represents, obsolete. Hugo frames the whole story as a farewell to the Middle Ages. The old world, beautiful and brutal, is ending. The novel mourns it and indicts it at the same time.