The Nazis belonged to the National *Socialist* German Workers Party in name only. In general, fascism in both Italy and Germany was marked by fairly pro-business policies. They were also fairly conservative in orientation – getting the bulk of their support from the middle classes up, and establishment institutions such as the church and wealthy capitalists (industrialists and landowners).
Pseudoramus also presents a nice summary of a time-consistent definition of right vs left in political economy:
…… historically, ‘pro-business’ or ‘pro-property’ fits the definition of the right in politics much better than ‘laissez-faire’. Businesses everywhere and always want pro-business policies — not laissez-faire, unless that happens to be consistent with pro-business at that point in history.
For example, when tariffs were considered beneficial for business, the pro-business party in the USA supported them during the 19th century, and the more populist party wanted to reduce or eliminate them. It was the same in the UK: the liberals advocated free trade while the conservatives wanted protection. In 1901-2, the Tories sought to abandon free trade, but the liberals waged a successful populist campaign to keep it.
The common thread to the right in history is not laissez-faire, but the tendency to support business or property. The common thread to the left is to redistribute income and property.
You might also be interested in reading this fascinating story in FT on Spain’s struggle with the legacy of Franco, it’s long time dictator.