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.
"so she let herself be married to a little clerk of the Ministry of Public Instruction..."See in text(The Necklace)
Guy de Maupassant was strongly influenced by his uncle, the famous French author Gustave Flaubert (1821–1880). Mathilde Loisel in "The Necklace" sounds very much like the heroine of Flaubert's best-known novel, Madame Bovary. Flaubert's influence on his nephew was extremely powerful. He would not allow Maupassant to publish until he felt satisfied with his writing. Flaubert is known as the leading exponent of literary realism in France. Maupassant's story can be seen as an example of literary realism, which is largely a reaction against Romanticism. The main characteristic Emma Bovary and Mathilde Loisel have in common is dissatisfaction with their boring lives, including their boring husbands. "The Necklace" can be read as a criticism of romanticism.
"She was prettier than any other woman present..."See in text(The Necklace)
Madame Loisel is possibly described as prettier than any other woman present because she is still so young. Most of the guests would belong to an older generation. The husbands would be middle-aged men who held important positions in the world, and their wives would be in approximately in the same age category. The women would all be wearing more expensive clothing, but Mathilde's youth and natural beauty would more than rival their artificial elegance.
"since with women there is neither caste nor rank..."See in text(The Necklace)
Guy de Maupassant was also heavily influenced by the German philosopher Arthur Schopenhauer. What Maupassant says about women here seems to come directly from Schopenhauer's cynical essay "On Women," in which the German philosopher quotes Napoleon as saying: "Les femmes n'ont pas de rang," which could be translated as "Women have neither caste nor rank." That is to say, a poor girl can marry a rich man and rise into the upper class if she has "beauty, grace and charm."
The wraps the women wore to the ball would not have been long coats or shawls but garments long enouigh to cover their bare necks, backs, shoulders and arms. This suggests that most of the women, including Mme. Loisel, were following the current fashion in wearing gowns that revealed a great deal of flesh above the bosom. It also explains why Mme. Loisel was so anxious to borrow that diamond necklace from her friend Mme. Forestier. The necklace would show to its best advantage against her bare chest, and in turn her beautiful neck would show to its best advantage against the necklace. However, she certainly would need something warm to cover her decolletage when she went outside, because the ball was being held on January 18th, which was well into winter.
"And she smiled with a joy that was at once proud and ingenuous..."See in text(The Necklace)
It seems odd that a wealthy woman like Mme. Forestier would own a necklace made of paste--a phony necklace. There is perhaps a suggestion of some secret guilt in her past. In the Sherlock Holmes story "The Adventure of Charles Augustus Milverton," Holmes is trying to bargain with the blackmailer Milverton in behalf of Lady Eva Blackwell. Milverton refuses to lower his demand for seven thousand pounds for some incriminating letters. He rejects Holmes' assertion that Lady Eva doesn't have that much money. He predicts tragedy unless she comes up with the full amount, and says: "And all because she will not find a beggarly sum which she could get by turning her diamonds into paste." Perhaps this was a common way for wealthy women to raise money without their husbands' knowledge. Mme. Forestier would have had to keep the phony necklace and wear it occasionally for her husband to see that she still had it.