Cafe Procope
It was opened in 1686 by the Sicilian chef Procopio Cutò also known by his Italian name Francesco Procopio dei Coltelli and his French name François Procope it became a hub of the French artistic and literary coterie in the 18th and 19th centuries.
It occasionally is called the oldest café of Paris in sustained operation however; the genuine café closed in 1872 and did not reopen as a café until the 1920s, so the claim of oldest café in incessant operation is not absolutely valid.