He claimed his first of two aerial victories in the Battle of France on 20 May 1940. Ostermann was appointed the commander of a "Rotte", an element of two aircraft, with "Unteroffizier" (non-commissioned officer) Fritz Marcks as his wingman. The "Schwarm" (flight) led by "Oberleutnant" (Senior Lieutenant or First Lieutenant) Günther Scholz engaged eight French Morane-Saulnier M.S.406's fighters near Amiens with Ostermann, Marcks and Scholz claiming one each. His second aerial victory was achieved over a Curtiss Hawk-75 on 26 May 1940. In a head on firing pass two 20mm shells tore off large parts of the aircraft's tail fin, which then collided with Osterrmann's starboard wing. The French pilot was observed to bail out with Ostermann managing to make a safe landing.