This character might well be the only stock type that Tolstoy puts into the book. There's a whole subgenre of 19th-century novels dealing with the strange situation of women who are part of a prosperous household but are neither members of the family, nor straight-up servants. These women are governesses (check out Jane Eyre, or Jane Fairfax in Austen's Emma, or Becky Sharp in Vanity Fair), or companions (like Miss Briggs in Vanity Fair or Jo March in Little Women). Everyone is always stressed about the status of these characters, and – just like with Mlle. Bourienne – some of the anxiety is that the governess will somehow get involved with the man of the house, which is bad because… um, class disparity, we guess? This is one of the things that doesn't translate too well across centuries.