There are really only three characters seen in "The Necklace": M. Loisel, Mathilde Loisel, and Madame Forestier.In regards to this question, M. Loisel is unimportant.
Madame Forestier is a rather flat and static character. She is a flat character given the author does not provide much information about her at all. All readers know is that she is rich and went to convent with Mathilde. Madame Forestier is also a static character given she does not undergo any change over the course of the story.
Mathilde, on the other hand, is a round and dynamic character. She is considered a round character because the author provides much information about her. In fact, the first two paragraphs offer readers a very straightforward characterization of her.
he girl was one of those pretty and charming young creatures who sometimes are born, as if by a slip of fate, into a family of clerks. She had no dowry, no expectations, no way of being known, understood, loved, married by any rich and distinguished man; so she let herself be married to a little clerk of the Ministry of Public Instruction.
She dressed plainly because she could not dress well, but she was unhappy as if she had really fallen from a higher station; since with women there is neither caste nor rank, for beauty, grace and charm take the place of family and birth. Natural ingenuity, instinct for what is elegant, a supple mind are their sole hierarchy, and often make of women of the people the equals of the very greatest ladies.
This detailed description proves Mathilde to be a round character.
Mathilde is also a dynamic character. A dynamic character is a character who undergoes change over the course of a story. Readers can see the dramatic change that takes place in Mathilde through the narrative provided about her at the end of the story.
Madame Loisel looked old now. She had become the woman of impoverished households--strong and hard and rough. With frowsy hair, skirts askew and red hands, she talked loud while washing the floor with great swishes of water. But sometimes, when her husband was at the office, she sat down near the window and she thought of that gay evening of long ago, of that ball where she had been so beautiful and so admired.
Essentially, Mathilde begins the story as a beautiful and jealous woman, thinking that she is living in a world beneath her. By the end of the story, she has come to understand her place in life as very different.