Let’s rephrase this slightly. The question is WHO, not what, the German military feared the most in World War Two. The answer was given by Adolf Hitler himself, in 1942 (and he was following declarations from several of his own generals and marshals).
At Bir Hakeim in May June 1942, 3,750 French prevented the entire Afrika Korps and Italian armor to encircle the British army. The stakes were so high, Rommel went to the front line and exposed himself to French fire. He said: “The fate of my army depended upon it!”. Actually, it was the fate of the entire Thousand Year Reich: if Rommel had encircled the British Eight army, there was no significant allied force all the way to eastern India. The Nazis planned to seize Palestine, kill all the Jews, and then grab Iraqi oil: the Nazis needed oil desperately, be it only to have enough to train their pilot and motorize their armies. French Legionnaires counterattacking at Bir Hakeim. The entire French army had burrowed in the sandy desert.
The resistance of general Koenig at Bir Hakeim lasted three weeks, long enough for the British army to escape. Bir Hakeim was more crucial than the battle of Thermopylae: the Eight Army lived to fight another day, and crushed an extended Afrika Korps a few months later, on the border of Egypt.
Hitler told his cabinet that Bir Hakeim was one more demonstration that the French were the second best soldiers after the Germans, and that is why France should be completely destroyed. (His cabinet pointed out that doing this would guarantee that Germany would lose the war. Hitler had to agree.) After the war, Generalmajor Friedrich von Mellenthin wrote, “In the whole course of the desert war, we never encountered a more heroic and well-sustained defence“
As the Nazis kept on pointing out, especially after they got defeated, it is the French who attacked the Nazis in 1939, not the other way around. French diplomacy stiffened the Polish spine and then persuaded the British to add an addendum to the Franco-Polish Treaty (Britain had sobered up from the fall of the Spanish Republic). The Nazis replied by making their alliance with the Soviets official. When the Nazis attacked France, in May 1940, they were using Soviet oil. Prior, they had used US/Texaco oil…
Why is this so important? First, the Jews and the nascent reborn Israel would have extinguished. Second, with Iraqi oil and the entire Arab world to help them out, the Nazis could well have cut off the US Lend Lease line to the Soviet Union, crucial to Stalin. Third, the performance of the Luftwaffe would have climbed considerably, with enough oil to train pilots, and the main problem with Nazi jets, gas guzzling, would have been less of a consideration (and more importantly getting some rare minerals the Nazis needed for jet engines’ alloys). Fourth, Stalingrad would not have happened as its strategic importance, holding the left flank of the drive to Baku oil fields, would have been irrelevant.