On 10 November 1940, Oesau succeeded Wilhelm Balthasar as "Gruppenkommandeur" of III. "Gruppe" of "Jagdgeschwader" 3. With 39 victories he was currently the 4th highest scoring fighter pilot behind Helmut Wick, Werner Mölders and Adolf Galland. On 5 February 1941 he shot down a Hurricane over Desvres, France, his 40th victory. He was awarded the Oak Leaves ("mit Eichenlaub") to his Knight's Cross next day. It also earned him a second entry in the "Wehrmachtbericht". In early 1941, JG 3 returned to Germany to replace their Bf 109 'Emils' with the new 'F' variant ("Friedrich"). However, Oesau disliked the Bf 109F and kept flying his 'Emils' for some time. JG 3 returned to France in May 1941 and Oesau added two more kills on 16 May and 28 May bringing his total to 51.