These earliest pictures of Jerusalem were taken in 1844 by French photographer and draughtsman Joseph-Philibert Girault de Prangey (1804 – 1892), who was active in the Middle East. In 1844, Jerusalem was a small town with a population of 15 thousand people on the outskirts of the Ottoman Empire. Remarkably, his photographs were only discovered in the 1920s in a storeroom of his estate and then only became known eighty years later.
According to Wikipedia, Girault de Prangey studied painting in Paris at the École des Beaux-Arts and in 1841 he learned daguerreotypy, possibly from Louis Daguerre himself or from Hippolyte Bayard. Girault de Prangey was keenly interested in the architecture of the Middle East, and he toured Italy and the countries of the eastern Mediterranean between 1841 and 1844, producing over 900 daguerreotypes of architectural views, landscapes, and portraits.