“I think you’ll find there were all business class flights well in advance of Lufthansa’s Privatair service.
Air France and British Airways flew something called a Concorde regularly across the Atlantic for many years, a product specifically aimed at the time poor businessperson.”
But in truth, the BA/AF Concorde flights were not business class. They were one-class flights but they carried an “R” designator which denoted supersonic class. R class cost very much more than business class.
The Privatair flights chartered by LH, LX and KL are priced at or around the business class price.
AF’s Dedicate service which serves the oil and gas industry is operated by two-class narrow-bodied Airbuses.