Although an eNotes Educator is unable to provide an "essay" for you of a particular word length, I can certainly deal with some of the elements of critical appreciation for you in regards to Maupassant's "The Necklace" and point you to some of our expert pages on the subject so that you can use both my answer and our other pages as secondary sources for your own essay.
First, let's explore what it means to provide a "critical appreciation." Taking these two words separately will give us the answer. If something is "critical" it should NOT give us the negative connotation based in our society. No, if something is "critical" it simply judges the value of something. Further, if something is an "appreciation" it focuses on that positive value, focusing mostly on that piece of literature's strengths.
Now it is appropriate to begin a critical appreciation of Maupassant's "The Necklace" by noting how often it is used as an instructive tool in the classrooms of education. It is of INCREDIBLE value to students studying literature. In regards to why, its provides ample opportunity to discuss many literary elements.
First, let's look at the element of setting. Setting always has to do with the place and the time. In regards to "The Necklace" it is appropriately set in the late 1800s in Paris, France. The main character's dreams and daydreams show what the life of the most affluent in France must have been like and how it is juxtaposed with the tedious work that she must do in her daily life.
Secondly, Maupassant's story is a perfect way to teach the elements of style such as point of view. It is well known that the narrator in the story is "third-person omniscient" in that he/she knows absolutely everything about the character and is willing to tell it to us, the readers.
Next, "The Necklace" provides another opportunity to teach style in regards to use of symbolism. The biggest symbol in the story is the necklace itself. It represents both Madame Loisel's greed and her superficiality. Not only is the necklace "not real," but neither is Madame Loisel, ... as she dresses in fancy clothes and goes to balls. Just look at her reaction when she first sees the necklace:
Her heart beats covetously.
Further, the story gives good examples of the use of irony, specifically dramatic irony. What we expect (especially in regards to the "expensive" necklace) certainly does not happen. The necklace turns out to be a fake and, in that, is a big surprise and one of the best ways to teach dramatic irony in literature.
Finally, it is perfection in regards to teaching the concept of theme. So, let's look at the main theme of appearance vs. reality. One needs to look no further than the necklace itself. Its appearance is one of extreme wealth. It's reality is one of superficiality. Now extend the theme to the character of Madame Loisel (whose name, by the way, is supposed to mimic the french term for young, unmarried lady "mademoiselle"). Her appearance is one of extreme wealth. Her reality is one of both superficiality and of lower middle class gumption. Even further, the entirety of French society values appearances too much, so we can go beyond the concept of character to reveal the theme in regards to French society as well.
Thus, as you can see, it isn't difficult to critically appreciate this story. It has been used over and over again in classrooms around the world and translated into many, many languages. It has truly stood the test of time and, therefore, has become a classic.