After seeing the live-action movie, there are some thing I thought about. I haven't really researched for facts, but here's the thing.
So in the live-action Beauty and the Beast, it was revealed that Belle's mother was one of the victims of the plague in Paris. I was thinking that Quasimodo's mother could be pregnant while also be a victim of the plague and somehow survived, then gave birth to a deformed child (Quasimodo), then being hunted by those men (seen in animated Hunchback of Notre Dame) because they were gypsys and they survived the plague and must be quarantined or some sort.
That was my analyzation, please confirm the timelines and stuff, because I haven't researched what time did the "Hunchback" happened and if it happened the same time as the flashbacks of the live-action Beauty and the Beast.