NOTE: this quest will not appear in your quest log.
Baudin tells you that his sister, Audia, has become cursed by some unknown force and craves the bloody raw meat of coeurl. Baudin is very concerned with his sister's well being and wishes he could do something to help. He mentions that Audia's fiance, Albrecht, prays at the Cathedral every day for her well-being.
Head to the Cathedral in Upper Jeuno and speak with the minster Mailloquetat for a cutscene with Albrecht, who tells you that none of his prayers have been answered and that his fiancee is still cursed.
Return to Baudin who will ask if you have any news of his sister's condition. No matter what you say, Albrecht appears and inquires if there were any changes.
(Side note: an unreferenced girl child NPC turns up again, named Alista. She also appears in the Cathedral above, at the end of the scene with Albrecht and Mailloquetat.)
Travel to Ru'Lude Gardens and speak with Neraf-Najiruf, in the Jeuno guards' room (G-7), who tells you about a similar problem which was cured by a magical torch. He hands you the Ducal Guard's Lantern (key item) and asks you to light it in Eldieme Necropolis. (Various missions/quests, including the Promathia mission Below the Arks, will take priority for this NPC. Neraf-Najiruf will first talk about the broken crystals at the crags or some other quest. If he does, just talk to him once again and you'll get the lantern.)
If after talking with him Neraf-Najiruf, he only mentions that "One time, a rookie of ours got cursed in the necropolis of Eldieme, and I didn't know what to do." then its likely you've not spoken to all of the NPCs the correct amount of times. Baudin, then Mailloquetat (for a cutscene), then Baudin again (another cutscene) and now Neraf-Najiruf should give the quest.
NOTE: If you're soloing this quest, for this next part, having a Magicked Astrolabe in your possession is required -- otherwise you'd need another player to open the various gates in the Eldieme Necropolis for you.
You must travel to four braziers in the following order. WARNING: If you visit a brazier out of sequence, your progress with lighting the lantern will be completely reset, forcing you to start over.
First Brazier: Southwest, Location F-9
Second Brazier: Northeast, Location H-7
Third Brazier: Northwest, Location F-7
Fourth Brazier: Southeast, Location H-9
After touching the first brazier in F-9, you will receive a message saying, "The Ducal Guard's lantern lights dimly." Find your way to the second brazier in H-7, and after lighting it you will receive a message saying, "The light of Ducal Guard's lantern has intensified." Head to the third brazier at F-7 and you will receive the same message as with the second brazier. Finally, the fourth and last brazier in H-9 you will give you the message, "The Ducal Guard's lantern is fully lit!"