Answer: We don't know; the movie never told us their names
Quasimodo's parents were mysterious characters. We don't know why they came to Paris, where they lived before, or why they left where they were living before. We only see them traveling up the Seine River to the core of Paris. They got off the boat they were in and were suddenly stopped by Judge Claude Frollo. After Quasimdo's father was arrested, we never heard nor saw anything about him ever again. We saw Quasimdo's mother's death, and her body being carried into the church by the Archdeacon.