The first thing you will need to decide is what meter to use in writing the poem. As this is an exquisitely crafted Parnassian story, in which pathos is developed by precision of details and a sort of situational irony rather than by sentimental language and melodramatic speeches, you should choose a verse form associated with a similar literary style in English, perhaps blank verse (i.e. unrhymed iambic pentameter), heroic couplets, or a French form like a villanelle in which you can use a refrain about the necklace itself, to express its weight in the characters' lives by repetition. Free verse would fail to give a sense of the structural precision and formality of the story.
Next, you need to decide whether you are writing for an audience familiar with the story. For example, if you look two very good models, Tennyson's "Ulysses" and "Lotos-eaters", both presume the reader knows Homer, and thus the author can focus on the nuances of a single experience rather than simply retelling the entire narrative. If the reader is presumed unfamiliar with the story, you might recast the entire narrative as a ballad.
As you write the poem, you want to focus on three major events, skipping much of the background, as relatively short, non-epic poetry is about peak moments of emotion; these three events would be Mathilde's moment of triumph at the ball, her discovery of the loss of the necklace, and her final discovery that the necklace was fake.