The mono-dimensional seating plan of the 1700s French parliaments is an impoverished paradigm for analysing later political movements.

Weinmar Germany was deeply tri-furcated between Socialist, Nationalist and Catholic political identities.

The National Socialist German Workers Party was an explicitly cross-over movement ( like Reaganism or MAGA in the USA), but a majority of members were drawn from the Socialist camp and a minority from the Nationalists.

So was Nazism "Left" or "Right" wing?

The answer is "yes". More "Left" on economic and religious matters, more "Right" on foreign policy. This framing is not particularly useful, except for smearing contemporaries.