While readers will correctly understand that "paste" in this context means a "fake," this is based on one of the additional meanings of the word "paste." When used as a noun, "paste" can refer to a heavy, clear-flint glass that is used for making imitation gems, such as diamonds.
Compared to a louis or a franc, the sou is the least valuable form of currency from 19th-century France. This means that she has become extremely aware of the value and amount of money she has, and she does not want to spend anything unnecessarily.
Garrets are small rooms in the roof of a building. Due to their being small, and typically dingy, they were the cheapest rooms to rent and served as homes for many of the poor.
The deep embarrassment they feel at having failed provides insight into their rationale for not admitting that the necklace was lost in the first place. Despite the friendship that Mathilde has with Madame Forestier, it appears that social obligations and class divisions run so deep in society that they would rather make themselves sick trying to solve the problem instead of admitting their mistake.
"attaches of the Cabinet..."See in text(The Necklace)
An "attaché" is someone who serves on the staff of someone else, an establishment, or an organization. The "Cabinet" here refers to part of the governing political body in Paris. These details serve to remind readers that Mathilde is participating in a high-end, aristocratic ball.
"her heart throbbed with an immoderate desire..."See in text(The Necklace)
The original French here can also be translated as, "her heart beat covetously." The notion is that her "immoderate desire" represents greed and her belief that she should live like her friend Madame Forestier.
This word choice is important because "fled" means to run away from a place of peril or danger. This gives the impression that Mathilde is afraid her friend might change her mind.
Satin is a smooth, silky material that is fairly expensive and objects made of this material generally give the impression of luxury. Fine pieces of jewelry are often contained in such boxes to protect the craftsmanship.
"the economical clerk..."See in text(The Necklace)
The choice of "economical" here characterizes Monsieur Loisel in two ways. First, it has a positive connotation that suggests he is efficient with spending money and good at his job. This contrasts with the second connotation (which Mathilde likely intends) that negatively characterizes him as cheap and unwilling to spend any money.
This is shorthand for a convent school. Many schools like these were attached to a convent and run by the nuns who lived there. The student population typically consisted of primarily girls. Since she knows her rich friend from school, it is possible that Mathilde's friend acquired her wealth and status through marriage.
Mathilde is not only imagining the objects that she would like to possess, but she is also considering the social interactions and behaviors she wishes were a part of her life. "Sphinxlike" refers to something that is mysterious or difficult to understand. In her mind, only these kinds of inscrutable smiles are appropriate for upper-class persons.
When Maupassant was writing, the term "oriental" was used to refer to any culture, region, or state located to the physical east of Europe, the Mediterranean, and generally lands east of the Christian world at the time. Mathilde uses it simply to refer to her desire for exotic and expensive possessions.
"outside her high-necked waist..."See in text(The Necklace)
The original French is sur sa robe montante. She is wearing one of those dresses which cover the neck almost to the chin. She is improvising by fastening the necklace around this high collar, but she can see how it will look when she is wearing a low-cut dress at the ball. The necklace will call attention to her beautiful neck, throat and bosom. Although Mathilde has never owned expensive jewelry, she has an instinct about such things and has undoubtedly imagined wearing all sorts of distinctive jewelry while indulging in her fantasies about the privileged life she felt born to enjoy.
This choice of words suggests that the weather outside is extremely cold--especially at four o'clock in the morning. Madame Loisel was anxious to put on her wraps, and she leaves in a hurry before the other women in their "costly furs" could see her in "the modest wraps of common life" and possibly ridicule her for wearing such cheap attire.