Oesau got his first World War II victory during the Battle of France on 13 May 1940, when he claimed a French Curtiss P-36 Hawk over Halsteren in the Netherlands, earning him the Iron Cross 1st class (). On 31 May, he claimed three Spitfires during a patrol North West of Dunkirk and next day he claimed a Bristol Blenheim. On 13 June 1940, he shot down the last French aircraft kill claimed by JG 51, a French Amiot bomber. By the end of hostilities in France on 25 June, his World War II tally stood at 5 (13 including Spanish kills).