Lets suppose the Germans take 6 months rather than 6 weeks to defeat the French. The French Government, meanwhile, relocates to Algiers and the French Military and Navy remain a threat from across the Mediterranean.
Italy doesn't enter the war (no opportunism on Mussolini's part) but rather focuses on dismantling Yugoslavia by stirring up Croatian secessionists.
Germany, with its nose more bloodied due to the war with France and needing to account for the threat of an Anglo-French assault on the soft underbelly of Europe, needs more time to organize before Barbarossa TTL. Ultimately, this never comes as Hitler falls down a flight of stairs. Goerring, now in charge, decides it'd be better to just focus on consolidating what's been taken. Stalin, being a very cautious man, opts not to start a war with Germany - though he does use the opportunity to pick a fight with Turkey.
Netherlands, Belgium, Luxembourg, North France, Denmark, Norway, and Alsace-Lorraine are incorporated into the Reich over time. Northern Transylvania is granted to Hungary, but Eastern Banat is provided to Romania as recompense. There is a government of the Petain-run "State of France" (in contrast to the Algiers based Third Republic) based in Paris.
Thoughts on this as a three-way cold war concept?