I presume by "National socialists," you mean the Nazis. They weren't particular advocates of the free market, but they weren't socialist in a meaningful economic sense. The Nazis did consider Communists as enemies. Their argument that Communism was an extension of Jewishness would be farcical if it weren't so tragic.

But for their part, the Communists would have been perfectly happy to make peace with the Fascists. They (correctly) recognized liberal democracy as a common enemy to their authoritarian dictatorships. Stalin didn't ally with western democracies until Hitler's surprise attack.

The only people in the National Socialist German Workers Party who believed in something resembling a form of socialism were those supporting Strasser and he and his ilk were amongst the first killed during the party's purges.

There's even a famous political cartoon of Hitler emphasizing the words Socialist and Workers for one crowd (blue collar) and National and German for the other (aristocrats). A more sophisticated quip might have been "what about National Bolshevists?" (aka "nazbols") but the short answer to that too is that if you try and add some red to your brown, it's still just another brown.