What is the conflict and denoument of the story of "The Little Prince"?
In French denouement (don't forget that middle e!) means unknotting or untying. This is a bit strange considering that as an English literary term, it basically has a meaning similar to resolution, which we might best explain as the tying up of loose ends at the end of a story: So we use the French word for untying to refer to tying up!
The theme of The Little Prince is that "what is essential is invisible to the eye." This comes from the scene where the Little Prince says farewell to the Fox:
And he went back to meet the fox.
"Goodbye" he said.
"Goodbye," said the fox. "And now here is my secret, a very simple secret: It is only with the heart that one can see rightly; what is essential is invisible to the eye." (Chapter 21).
The conflict that arises near the end of the book is the need for the narrator to let The Little Prince go. In the real world, a pilot who survived a crash landing in the Sahara desert and met a seemingly defenseless child there would want to rescue that child and bring him back, to adopt him as it were. However, The Little Prince is not what he appears to be--he only appears a child. He has a life he must return to, responsibilities he must take up once again. He must protect his Rose. He has mysterious powers, such as his knowledge that the narrator has fixed his airplane before the narrator informs him of this fact. But then The Little Prince adds, "I, too, am going back home today . . . .It is much farther. . . It is much more difficult . . ."(82). In order to return home on this anniversary of his arrival on Earth, The Little Prince must seemingly die--at least this body must die. He does not want the narrator to see his apparent death, which will be by snakebite; The Little Prince tries to sneak off to meet this fate alone; however, the narrator follows him, and is told:
"It was wrong of you to come. You will suffer. I shall look as if I were dead; and that will not be true . . ."
"You understand . . . It is too far. I cannot carry this body with me. It is too heavy." (86, emphasis added).
Having mysterious knowledge of events he can not see and the ability to depart this world by appearing to die while not really being dead make The Little Prince a bit of a Christ-symbol. Perhaps he has saved the narrator from becoming like the rest of the "grown ups."
As for the denouement (pronounced vaguely like day-new-moan--only with a nasal constriction of the throat during the "oan" part)--there is not much: the narrator informs us that six years have passed and that he knows the Little Prince "did go back to his planet, because I did not find his body at daybreak" (89). The discussion about whether or not the sheep has eaten the Rose or not (of course the Rose is safe) serves to stress the theme that what is essential is invisible to the eye: "Look up at the sky. Ask yourselves: Is it yes or no? Has the sheep eaten the flower? And you will see how everything changes . . . And no grown-up will ever understand that this is a matter of so much importance! In line with the Christian symbolism of a savior who teaches us what is important and then departs our world, the final note at the end of the book--in fact--after--the end of the book (note the smaller typeface) asks us to watch for the return of The Little Prince--reinforcing a gentle resemblance to Christ.
The major conflict in the story is arguably both the little prince and the pilot's quests for the ideal, something they learn through their respective journeys is fairly unattainable. The denouement of the story leaves the pilot unable to find the little prince's body, concluding with a fair amount of certainty that he must have returned to his asteroid. The pilot (as narrator) then asks his readers, if they ever visit the desert spot from which the story is narrated, to please inform him if they see any signs of the prince.