As it concerns the foreign policy of such a Germany and its effects on the world, this is in all likelihood a case where butterflies are smoothed out and the lack of the Nazis in power makes a radical difference anyway. I am not willing to re-open the Germanophiles vs. Germanophobes eternal flamewar yet again whether the Western democracies would be willing (and ought) to make a compromise peace with a post-Nazi Germany in 1940-43, so I focus on the pre-WWII scenarioes.
Now, the foreign policy of any non-Nazi, non-Communist 1930s-1940s Germany would be centered on undoing the Versailles settlement, by uniting German minorities with the Reich, revising the Polish border, achieving military parity with the West, and ending the reparations. Other main objectives would be to rebuild an economic-political sphere of influence in Central-Eastern Europe and containing Soviet Russia. Since those objectives would be genuine and not just stepping stones to the Lebensraum and military domination of Europe, they are going to be pursued with rather more tact and moderation than Hitler did.
Specifically, this Germany does not invade Czechoslovakia after Munich or makes a sensible compromise after Hitler did it, and is willing to leave Poland independent if it gets Danzig and the Corridor back. Since all the reasons for Britain and France to pursue appeasement of Germany in the 1930s would still be in place, we can only reason that without Hitler's invasions of Czechoslovakia and Poland that broke it down, such a strategy would be ultimately successful and produce a stable Anglo-Franco-German detente and a settlement where all sensible Versailles grievances of Germany are settled peacefully, it becomes a satisfied power, and WWII as we know it is averted. At that moment, the main issue becomes whether the other potential rogue powers, Soviet Russia and Japan, are still going to unleash a WWII.
Now, a broad scenario description, picking one among the likely PoDs:
ITTL a couple key transfers that that put anti-Nazi conspirators out of key positions in the Heer hierarchy during early 1939 do not occur. The German officer corps, despite their strong anti-Pole feelings, are wary to stage a general conflict with the West about Poland. The realization spreads that Hitler is not out for any sensible compromise to return the "rightful" 1914 borders to the Fatherland, he wants war to conquer all of it and open set up Lebensraum shop. The old pre-Munich coup plans are reactivated, the Heer stage a successful anti-Nazi coup in late August 1939. The Danzig crisis winds down with the regime change.
An Heer junta takes over, purges the Nazis, cuts expenses to stop the budding economic crisis. No charismatic leader or really talented ruler emerges in the junta, and it is split between neo-Wilhelmine and pro-democracy sympathizers, so it makes tentative advances to the leaders of disbanded democratic parties for a power-sharing compromise. They broker a monarchical restoration and continuing influence and autonomy of the officer corps in exchange for return to democracy. The party leaders are willing to deal, the only serious motive of attrition is the fate of the SPD and the trade unions. Elements of the officer corps oppose their legalization, in the end a compromise is reached that makes them partially legal with some limitations.
A new constitution is drafted and approved by plebiscite that enacts a "controlled" conservative democratic restoration under a constitutional Hohenzollern monarchy: civil rights are restored, Conservative, Liberal, and Christian Democratic parties and trade unions are legalized (Nazis and Commies are banned), SPD and socialist trade unions have limitations to their activity (but these are revised away after a few years), a modified Weimar constitution and electoral system are established to restore a British-style constitutional monarchy, reinforce the executive, lower political fragmentation and instability, and ban extremist parties. The Wehrmacht is guaranteed the role of last-instance guardian of the political system in a constitutional crisis (which is revised away after a couple decades) and ample autonomy from parliamentary oversight. Louis Ferdinand of Prussia becomes Kaiser. Federal autonomies are restored, but borders of the Landers are rearranged. Jews get civil rights back. The government is responsible to the Reichstag but it gets substantial safeguards to reinforce it (constructive no confidence, ability to pass legislation with a vote of confidence and determine the parliamentary agenda, a non-proportional electoral system, limited ability to issue decrees). The first Reichstag election returns the majority to a center-right coalition.
After it has stabilized, the new German government goes to Britain and France and proposes a bargain: the Czech are restored to democratic self-rule in internal matters, with a confederal association to Germany that deals with foreign matters, security, economic and currency union, in exchange for Western support for sensible German claims in Poland. Their maximum program are the 1914 borders, their minimum one is Danzig, a land connection to East Prussia, and a revision of the Upper Silesian border. They also offer a renewed naval limitation treaty to Britain, and a reaffirmation of the existing border to France.
Under the table, they effectively make a secret offer to Britain and France: let Germany satisfy its last Versailles grievance and build a sphere of influence in Central/Eastern Europe by peaceful means, and they shall guard it against the Soviets and make not more trouble in Europe.
The democratic/monarchical restoration (and the end of anti-semitism) and the autonomy offer for the Czechs give back Germany some of the goodwill that Hitler had burned with the betrayal of Munich. Therefore Britain is willing to revive the appeasement strategy. The deal is accepted and the Munich II conference convenes to discuss the Polish borders problem. Eventually a compromise is reached about the return to Germany of Danzig, a strip of territory in southern West Prussia through Torun that connects Pomerania and East Prussia (where German presence was concentrated before 1919), and a slice of Upper Silesia according to the 1921 British-Italian proposal. Poland fumes and rages but eventually backs down and accepts the deal, rather than facing a war with Germany and maybe Russia alone.
At this point a potential major divergence about the course of the world exists according to Stalin's and Japan's actions. Stalin may either be cowed by Western-German detente, or be roused to pre-emptive attack. Japan may be cowed too or go for its usual kamikaze expansionist rampage.
If they are cowed, relations between Germany and the Western powers gradually thaw and Western-Central European integration emerges fueled by economic cooperation, still broadly confederal in scope but less far-reaching and supranational than OTL EU. Germany gradually becomes the economic giant of Europe and gets pretty much all the influence it wanted by peaceful means.
Mussolini eventually builds a good enough military and attacks Yugoslavia in cooperation with Hungary and Croatian separatists, he gets Dalmatia, Montenegro, Kosovo, and a satellite Croatia but Western powers and Germany join into containing him from further aggressions. Italy gradually democratizes when he dies.
An indecisive war occurs between Hungary and Transylvania, the great powers enforce a settlement much like the Second Vienna Award.
Japan exhausts itself fighting Chinese insurgency for a decade, eventually pulls out of China proper, but keeps Manchuria. Chinese Civil War occurs, ending in a division between Red North China and capitalist South China.
Russia follows a PRC course after Stalin dies. The USA still become a global powerhouse, but the world remains multipolar, with USA, Germany, and Russia as the top tier powers, followed by Britain, France, Japan, Italy, and South China.
(for the sake of brevity, I skip the analysis of the more complex case where Stalin keeps the peace in Europe, but he still attacks Japan).
Alternatively, Stalin inteprets Western-German detente as a sign that the capitalist powers are closing on him, so he decides for a pre-emptive attack when he feels that the Red Army and Soviet industry are ready, sometime in 1942-43. A WWII much like our own occurs (but destruction is contained to Eastern Europe and the Middle East, and Stalinist atrocities in occupied territories occur instead of the Holocaust), with Stalin in the shoes of Hitler. Eastern Europe and the Middle East are overrun, but the European coalition, supported by USA Land-Lease, stalemate the Red Army someplace in Poland & the Balkans and gradually beat it back. When the Euros get deep in Soviet territory, Russian generals stage an anti-Soviet coup and make a Brest-Litovsk peace.
Japan surely tries to exploit the situation, it may either backstab the Russians in RFE or the Anglo-French in South East Asia. if the former, it comes out of the peace table with Outer Manchuria, the Western powers don't want a Japanese China but Communism is the devil, so they give maximum support to GMD against the Communists and the Ntionalists win the chinese Civil War. They pressure Japan to pull out of China, but recognize its other gains, so it keeps Inner Manchuria and Inner Mongolia and makes Outer Manchuria . If it goes south, events unfold pretty much as OTL, the Soviet defeat is rather quicker since America joins the anti-Soviet coalition.
A multipolar world emerges with the USA and a federal continental EU (forged by wartime cooperation) as the main superpowers, Britain as the "strategic partner" of either the USA or the EU, capitalist China has its rise accelerated by several decades, Japan may be a great power if it was not beaten down to a USA vassal.
Culturally it is a rather different world where Communism, not fascism, is demonized, Stalin's atrocities are the archetype of absolute evil, and far right ideas remain respectable much longer.