What is the basis of the story?
If you are asking what the moral of "The Necklace" is it is that appearance rarely equals reality, and pride often blinds one from recognizing that truth. For example, Mathilda sees her husband as a commoner, someone whom she had to marry but who does not represent her taste for the finer things in life. Because of her self-absorption and superior attitude, she does not recognize the wonderful qualities in her husband--he is willing to sacrifice his own desires to buy her a dress and even to go to an event that does not especially interest him because he knows that she will enjoy it.
Mathilda is also blind to the fact that the necklace is fake. She is so enamoured with its glittering appearance and believes that because it belongs to her wealthy friend that it must be priceless. She sees only the shiny surface of things and people.
Finally, even at the story's end when Mathilda discovers that she and her husband worked all those years for nothing, the first person she thinks of and feels sorry for is herself. Once again, she fails to realize that the reality is that her loyal husband has done more than most would and has sacrificed just as much if not more than she has.
I am not completely sure what you mean by the "basis" of the story.
However, I think that you are probably asking what the basic facts are.
In this story, Madam Loisel is a woman who is dissatisfied with her place in life. She feels she deserves all kinds of good things in life, but she does not have enough money to afford all of these good things.
When she is invited to a fancy ball, she feels that she must dress more fancily than she is able to. So she borrows a necklace from a friend.
She loses the necklace, but does not tell her friend that she has. She ruins her life trying to pay for the replacement that she buys.
In the end, it turns out that the necklace she borrowed was fake and she has ruined her life for no reason.
The basis of the story is the fact that the woman created her own fate as a result of wanting that which she could not afford. Mathilda was not happy with what she had in life. She wanted more and was unable to recognize the good things that she had.
Matilda borrows her friend's necklace and then loses it. She replaces it with one that had caused her husband o use up his savings and borrows money. She was honest to pay back the necklace, but deceitful in lying about it to her friend. Replacing it without telling the truth that she had lost it was the lie.
There are three ironies in the end. One occurred because she and her husband had worked extra hard and were now worn down by all the hard work. Matilda learns the necklace had been a fake. She worked all those years for nothing.
The other irony is that she had so much more before she had to have more. In the end she had caused herself a harder less appreciative life.
The other irony is that the person whom she envied for having everything, was happy with owning a fake necklace.
so i believe the story is talking about being content with what you have since she was dissatisfied with her position in life