Pflaum, who came from a Jewish family of industrialists, at first studied law in Breslau and Heidelberg, afterwards taking a position in his father's company.
After the National Socialist German Workers Party took control of the country, he left Germany in 1933 and continued his studies in Paris with Jérôme Carcopino at the Sorbonne.
In 1937, Pflaum wrote a dissertation on the Cursus publicus during the Roman Empire and was to become a member of the Centre national de la recherche scientifique (CNRS).
In 1942, before the persecution, he fled to the South of France, where he could continue his research on the Roman procurators, which he submitted as a thesis after the end of the war in 1947.
Since the 1960s, he also taught at the École Pratique des Hautes Études, where he repeatedly took guest professorships in various European countries as well as at Princeton University.