The common conception that National Socialism (and fascism in general) has nothing to do with socialism or communism and the French Revolution from which they sprang is wrong. The two groups of ideologies are quite distinct but have a number of important traits in common.
Naziism is commonly identified as...
a form of fascism, a right-wing ideology whereas socialism, particularly Marxism and communism are considered left-wing movements. The left vs. right association in the popular imagination is the result of a long propaganda war that has created the lasting impression that Naziism and socialism are mutually exclusive.
Adolf Hitler, the leader of Nazi Germany and the most famous proponent of National Socialism, vociferously denounced left-wing socialists (especially communists, who were seen as enemies of Germany). The Soviet Union, the world's first socialist country, was Nazi Germany's bitterest enemy on the international stage. Hitler described the USSR as a rotten house that would collapse as soon as Germany kicked the door in. Hitler made no secret of wanting to end the Soviet experiment by force. In Mein Kampf he further describes the lands of the USSR (and other Eastern European nations) as the "living space" required by an expanding Greater Germany. In keeping with Hitler's genocidal intentions, the Eastern Front of World War II would feature some of the most savage fighting during the war. In fact, it was the bloodiest confrontation between two peoples in human history and the theater where the military strength of Nazi Germany ultimately bled out.
The war between the Nazis and Soviets, while seeming to pit diametrically opposed ideologies against one another, was really a struggle between two different systems that both grew out of the French Revolution. During the Revolution, France was able to marshall unprecedented military strength by mobilizing its entire population through conscription and nationalist propaganda. The revolutionary government also seized control of manufacturing, rationed food and regulated prices. As the years went by and the wars dragged on, the revolution radicalized to the point that all conservative and even moderate opposition was suppressed. During the Terror the Committee of Public Safety killed thousands for crimes, real and imagined, against the revolution.
Ultimately the French Revolution would end in conservative reaction and the establishment of a dictatorship under Napoleon I. Posterity would be left to debate its significance and to interpret the various political forces it brought into the world. What no one could deny, however, was the incredible military strength the revolution was able to marshall. The armies Napoleon inherited rolled over the monarchies of Europe and could only be brought down by the combined strength of every other great power of Europe. It was a history lesson lost on no one.
When you look at Nazi Germany and the Soviet Union, they actually have a great deal in common with one another and with Revolutionary France. Both powers were totalitarian dictatorships ruled by one political party that used the power of the state to brutally suppress any opposition. Both the Nazi and Communist parties had, in fact, undergone multiple purges to remove all perceived rivals to their respective party leaders. In both countries those leaders used propaganda to create cults of personality around themselves. Heroic images of Hitler and Stalin were ubiquitous in their respective countries while the people came to regard the dictators as semi-divine figures.
No French leader ever went so far, but the antecedents of such demagoguery were there. Napoleon rigged plebiscites to claim nearly universal approval of his leadership. He had medals minted to spin failures like the invasion of Egypt into successes. Paintings by Jacques-Louis David depicted Napoleon as both towering statesman and brilliant conqueror, crossing the Alps on a stallion.
The deification of dictators speaks to another common thread between the Nazis, Soviets and French: the displacement of religion as a source of authority in all three societies. The French revolutionaries regarded the clergy of France as complicit in the subjugation of the masses under the old regime, the second estate conspiring with the first (the nobility) to plunder the third (everyone else). Robespierre, French leader during the Terror, recognized that banishing Christianity left a large whole in French culture. In response he tried promoting farcical cults of "divine reason" that failed alongside the revolutionary calendar. Old habits were just too strong.
Hitler and Stalin both encountered the same problem; their methods of dealing with religion delineate what the two regimes had in common and where they differed. As mentioned, both dictators offered themselves up as substitutes for Christ; however, the Soviet Union was an atheist nation that brutally suppressed the Orthodox church. Hitler tread more carefully. He was well aware of the fact that the Catholic Party formed the single largest voting bloc before free elections were suspended.
More importantly, the Nazi brand of socialism distinguished itself left-wing socialism by being culturally conservative. The Nazis, like the French during the Revolution, leaned heavily on the concept of citizenship. Under the old French regime, the state was the monarch (as Louis XIV famous put it) and the people were merge subjects. The Revolution redefined the state as the political embodiment of the nation: a geographic area characterized by a single culture, language and ethnicity. At the same time, the French Revolution also waged class warfare against the first two estates and attempted to remake French culture in ways that did away with traditions associated with the feudal system. Here lies the crucial distinction that separates the Nazis from the French and Soviets. The Nazis rejected class warfare while placing far greater emphasis on traditional culture and national identity. While socialist in the sense that they rejected the individualism and free markets of Britain and the United States, the Nazis took a more limited approach to economic planning than the Soviets, in the process preserving the traditional powers and privileges of wealth and aristocracy. The church enjoyed the state's respect in Germany, as long as it did not obstruct the national program. Thus the Nazis achieved something like the strength of Revolutionary France not by pulling down the pillars of traditional culture but by uniting citizens in a fanatical crusade against the two demonized enemies of the state: Jews and communists.