Before you go hunting for full-size images, consider the ethics and legality:

Maya zoomed in further. The resolution grain increased, but the details clarified. Jacob’s smirk wasn't carefree; it was strained. His eyes, usually hidden by the distance of a small preview, were rimmed with red, tired circles. He was holding a coffee cup that said "Get Through It."

This method works best for Public profiles. If the profile is private, you will only see the basic picture that is already visible to you, and you may not be able to access the full-size version if Facebook’s privacy restrictions are strict.