What if instead of accepting the armistice with Vichy france, Hitler had instead forced a peace treaty forcing france to join the axis, but also allowing france to raise a army and airforce and giving the power to Eugene Deloncle? Of course this would lead to the entire french africa defecting to free france earlier, but would this help the axis war effort?
I raised a similar idea on another forum. The prerequisites for this were basically to start treating France as an ally rather than a conquered nation, which he would not do IOTL. It would mean not taking A-L, not putting major military restrictions on France, not giving them an occupation cost, not requisitioning anything they wanted, not imprisoning/forcing into labor millions of French PoWs, not giving the Mark 1:20 value vs. the Franc, etc. Effectively say "Hey join the war as an ally under German command right now and you face no reprecussions of losing this war" and mean it, while also having them sign on to a customs union and some political control from Berlin. That might be doable, but the real question is whether the French government could get the country to be willing to flip side like that. Resentment against Britain was very high at that moment and the prospect of not having to face a reverse Versailles would be pretty powerful in July 1940, especially after the Mers-el-Kebir attack. If Hitler was willing to do that and piss off all the German military and public then France would probably go for it, I just don't see that happening given that he thought Britain was about to quit the war then he could enslave France. The question is would he be more willing after the failure of the Battle of Britain was lost? Say a Mediterranean Option in 1941 with all the concessions to France to get them onside as an ally? That might be doable for the French at that point, but Germany does seem somewhat weaker and the Nazi party and military would not be happy about giving France a pass when the general consensus of the public was enact revenge for Versailles in terms of a peace treaty; it was far better for German strategic interests to make major concessions to France and turn them into an ally, which would probably be enough to force Britain out of the war (Germany and France allied would mean the Mediterranean is lost to Britain and the Middle East turned into an active front thanks to the French Fleet), but the general attitude of Hitler's political base and the military was to punish France, not make them an ally, even if somewhat a puppet. Even a customs union in the long run would be hugely beneficial to German post-victory, but general Nazi attitudes weren't really known for being pragmatic once the war started.
A Franco-German Axis with Germany as the senior partner would be a powerful combination during and post-war, I just don't see Hitler as the guy willing to do it. Still if it were to happen that would bring the French fleet into the Axis, which when combined with the Italians fleet and German fleet would cause Britain enormous problems. Beyond that Spain would probably join the Axis because of the perception that Britain was now doomed, which means Gibraltar falls. With Gibraltar falling that means the Western Mediterranean is shut off to the Brits, which means Malta falls in 1941 not that much after due to the lack of convoy/club runs to Malta. The the Franco-Italian fleet and merchant shipping would be enough to take Egypt, open up a Syrian Front, take Rhodes, etc. The Mediterranean would fall apart for the Brits and the Middle East becomes an active Front with the Axis having the Mediterranean as a safe shipping highway, while the Brits have to supply from India and around Africa. Bad news for the Brits.