The answer below is a good one, I would like to add that her enviousness toward the life she does not have foreshadows the life that she will fall into later. She thought that her life was terrible and she was probably what we know as upper middle class which was far too meager a life in her opinion. These thoughts are what foreshadow her eventual fall into utter poverty. She complains that she has only one maid and dreams of having scores of them, when eventually she has to do all her housework herself. She day dreams about being beautiful and admired by all and in fact loses her admired beauty. The ease with which Mme. Forrestier lends the diamond necklace also foreshadowed the inexpensive nature of the thing, which we find in the end is in fact a fake.
There are several elements of foreshadowing in the wonderful story "The Necklace."
Start with the opening line: "The 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."
This lets us know fate will play a role, that slips will play a role, and that she really should look like a clerk, as she does by the story's end.
The first line of the second paragraph says why she dresses plainly; this is stated almost as a universal, and it will be true again by the end of the story.
A bit later, the story says, " She had no gowns, no jewels, nothing. And she loved nothing but that." This is foreshadowing through irony. She loves only that—and it will be taken from her.