Did British Airways or Air France use Professional Flight Engineers (non-pilot PFEs) on Concorde or were the flight engineers required to be pilots (not necessarily qualified to fly Concorde) who were trained and qualified/certificated as flight engineers?
Flight engineers were called "OMN" (officiers mécaniciens navigants) and had no pilot rating for Concorde. They were not required to be pilots at all.
PIC and copilot had to obtain the ATP licence and a "Qualification Concorde" (Concorde rating).
OMN had to obtain a "Brevet de Mécanicien Navigant" (Flight Engineer’s Licence) and a "Qualification Concorde" (Concorde rating).
You may confirm this by looking at BEA report for F-BTSC accident.
Licenses are similar:
- For pilots: ATP license and Concorde rating.
- For flight engineers: Flight Engineer license and Concorde rating.
This is confirmed in AAIB report for G-BOAF accident.
None of the civil aviation flight engineers I can think of from Latécoère to the FADEC introduction were ever required to be pilots.
See also: Did Flight Engineers progress to be pilots? a question from the early days of this stack.