The exact phrase is indeed not in the original text by Victor Hugo. It does come up in an 1871 play, The Bells, by Leopold David Lewis. In the text, there are several points where the character Mathias hears the sound of bells, a sign of his guilty conscience from having previously murdered a Jewish merchant who had bells on his sleigh. In particular, there is a final episode where Mathias has a dramatic breakdown as he relives the murder in view of the assembled crowd. An extract:
One o'clock strikes, and the moon shines. Ah! The Jew has already passed! Thank God! Thank God! (He kneels--a pause--he listens--the Bells heard without as before.) No! The Bells! The Bells! He comes! (He bends down in a watching attitude, and remains still--a pause--in a low voice.) You will be rich--you will be rich--you will be rich! (The noise of the Bells increases--the CROWD express alarm simultaneously--all at once MATHIAS springs forward, and with a species of savage roar, strikes a terrible blow with his right hand.) Ah! ah! I have you now, Jew! (He strikes again--the CROWD simultaneously express horror. MATHIAS leans forward and gazes anxiously on the ground--he extends his hand as if to touch something, but draws it back in horror.) He does not move! (He raises himself, utters a deep sigh of relief and looks round.) The horse has fled with the sledge! (The Bells cease--kneeling down.)
From a biography of Henry Irving, an actor and producer who performed the role many times (Sir Henry Irving: A Victorian Actor and His World (Bloomsbury, 2007), Jeffrey Richards, at p402):
After the Second World War, which can in many ways be seen to mark the watershed between the Victorian and the post-Victorian worlds, [The Bells] largely vanished from the theatrical repertoire and from the popular consciousness, so much so that the cry 'The bells, the bells,' which anyone up to 1939 would have known was a reference to Henry Irving and the play, came to be recognized thereafter as a reference to Charles Laughton as Quasimodo in the 1939 Hollywood film The Hunchback of Notre Dame.
The same attribution of the phrase is in The Oxford Dictionary of Plays (OUP, 2015).
Now, the 1939 Hunchback was tremendously popular, but it also does not include the exact phrase about the bells. He does have a repeated phrase in "Sanctuary! Sanctuary!", during his rescue of Esmeralda and taking her to the belltower. He then capers about the bells and demonstrates their tremendous sound. It is a roughly similar kind of bell-associated dramatic mania as in The Bells, but not for the same reasons, and not the same kind of bell. Still, I'm inclined to trust the cited authors for the transference of the phrase. Perhaps it's a case of viewers having a general impression of Laughton's performance but not recalling the specific quotations.