Fascist regimes have always supported free-market capitalism;
Incorrect. Fascist regimes such as Nazi Germany, Mussolini's Italy, and Jinping's China (today) ALL dictate to private industry. And only those who did the bidding of the state were permitted to own various industries.
For instance, a few years ago the FBI wanted Apple to help to unlock an iPhone. Apple rejected the FBI's request. That doesn't happen under fascism. Can you imagine Huawei telling the Chinese State Police that they wouldn't help or a German company telling the Gestapo to get lost? LOL. Yea, neither can I.
There is no such as free-market capitalism in a fascist society as all industry is subservient to the state.