Why does Claude Frollo kill Captain Phoebus?

In Victor Hugo's famous novel The Hunchback of Notre-Dame, Claude Frollo is the corrupt archdeacon of the titular Notre Dame Cathedral. Captain Phoebus de Châteaupers is the Captain of the King's Archers, and while he is not as bad as Frollo, he isn't such a great guy either.
We see Claude Frollo's dark personality in many ways, including when he becomes obsessed with and pursues Esmeralda relentlessly. And by pursues, I mean tries to kidnap her because he wants to possess her, like an object, so that no one else can have her. Phoebus saves Esmeralda from the attempted kidnapping, and she consequently falls in love with him. Later on, the two agree to meet up again; Esmeralda wants to tell Phoebus that she loves him, while Phoebus just wants to have sex with Esmeralda (he's already engaged to someone else).
Frollo finds out about their relationship and the possibility of Esmeralda having sex with someone besides himself, and he becomes enraged. He disguises himself and pays Phoebus to let him hide in the room where the two lovers are going to meet. Phoebus agrees to this because he has no money, and while he is seducing Esmeralda, Frollo jumps out and stabs Phoebus. Esmeralda faints, and when she wakes up, she has been accused of murdering Phoebus (who later turns out isn't actually dead). So essentially, Frollo stabs Phoebus because he is insanely jealous of him due to his obsession with Esmeralda. He also uses the incident as a way to frame Esmeralda for murder so that he can try to take her again while she's imprisoned.