Before any conclusions about "worst" can be made, one has to attempt to better define what is meant by "worst". IMO worst does not necessarily mean "least effort", or "smallest". To my mnd, the answer has to remain general, because of the general nature of the question, however, IMO "worst" probably equates to "most poorly managed"
To be honest, I dont know who is "worst", even in the terms I have tried to clarify. Perhaps it was France, perhaps Italy, or even Rumania, but it is hard to point the finger at any single nation.
If you look at France, it was the French who first worked out the theoryof how to defend with Infantry against Tanks. it was called the "Quadrillage system" and it was worked out by Weygand during the latter part of the BOF. people often overlook that approximately 1500 German A/C were lost over France in just 6 weeks of fighting, which is a loss rate to rival that which occurred in the BOB later that year.
Many people are critical of the Italians, yet, if you look closely at thair war effort, it pretty quickly becomes quite clear that their failures have been hammed up by both their opponents and their erstwhile allies. In the case of the Rumanians, few people know or realize that it was German formations, sent to bolster the Rumanians who broke at least at the same time as the Rumanian formations, and that the Rumanian formation defending the flanks at Stalingrad were expected to do that with just 6 75mm AT guns per Division. Rumanian forces were responsible for the capture of Odessa in 1941 (with only minor support from the germans), whilst the Rumanians contributed materially to the fall of Sevastopol. Finally Rumanian airpower was a significant proportion of axis air strength on the southern front of Russia right through until capitulation.
I am tempted to say the "worst" performers were the germans. There is no denying their combat effectiveness, but their management of their side of the war was attrocious. Take Hitlers decision to invade Russia. I know he had talked about it since Mein Kampf, but he had also berated Imperial Germany's mistake of undertaking a two front war, which is precisely what he did himself, when he invaded Russia. He failed to fully mobilize the german economy until it was too late, and never treated his allies as coalition partners in any sense of the word. The minor Axis partners (Rumania Hungary, Finland, and Bulgaria), were all essentially agrarian nations, who lacked the means to properly equip themselves. If they had been decently equipped by their german partners, they would have put up a better showing than they did