The irony of the cemetery
The Cemetery of Forgotten Books is ironically titled, because cemeteries are where dead people are interred into the earth, but instead of being buried, Carax's novel is saved by a young reader who picks it off the shelf and agrees to cherish it. Not only does that revive Carax's legacy and the story of his love for Penelope, but it also provides a sense of direction for Daniel's life.
The irony of the ending
If the story that Daniel reads is beautiful and poetic, but the reality of the author's life is traumatic and turbulent, then the ending represents Daniel's choice to pursue love and meaning through romantic commitment, even knowing the horrors that he might be signing up for. It's ironic, because the entire story seems almost designed to scare him, but because he loves Carax like his own family, he sees the beauty in Carax's tragic fate.
The ironic parents
Parents are supposed to be loyal, supportive, and helpful, but not for Penelope. Penelope's parents are cruel, and they are traitors in their own marriages—both Penelope's and Julian's parents are riddled by their affairs. They aren't supportive whatsoever—they treat Penelope like a dog, and they let her die while she begs them for help. They're such bad parents, they're almost anti-parents.
The irony of Coubert's identity
When Daniel discovers that his favorite author's books are being systematically located and burned, he is astonished, but not nearly as astonished as he is when he learns that Coubert is actually Carax himself, burning the books out of grief, having lost the love that inspired them. This irony points Daniel to an important discovery—when you're not expecting tragedy and it takes you by surprise, it can do serious damage. It's kind of like a warning to Daniel that unless he wants to become his "worst enemy," so to speak, he should stay aware of death and fate.
The irony of Daniel's name
When Daniel names his son after his favorite author, that ties their stories together in real life. It's a real life manifestation of the legacy of Carax's love for Penelope—which is ironic, because the baby that Penelope and Carax lost, that baby was named Daniel. Not only is Daniel's son named Julian—Julian's son is also named Daniel.
