This is a great question because it ties in with the profound biting irony of this great tale. The point of view is actually third person limited as the author chooses to zoom in on one character alone and narrate the tale from his perspective. The character chosen is Monsieur Lantin, who has the misfortune to lose his wife as she dies. However, the impact of this point of view is that we, like him, have to go through a process of piecing together what his wife was actually really like through the clues that we are given. The point of view then keeps us in the dark and forces us to re-assess our perspective and thoughts about Madame Lantin, her supposed simplicity and her mysterious ability to manage their income so well that they could afford treats.
As Monsieur Lantin realises that the jewels are not in fact fake, but real, and they were purchased for his wife by another man, he experiences the shock, shame and then the greed of having a large amount of disposable income. It is the choice of the point of view that enables us, the reader, to share with Monsieur Lantin's perspective as he goes on a voyage of discovery.