They weren't looking for cruise drag reductions; just takeoff climb improvements which would have required genuine relaxed stability - CGs back at the aerodynamic centre etc.
This entailed introducing artificial stability terms that would have been difficult in a purely analogue system such as the basic Concorde controls, so they decided to go digital.
Sidestick or conventional control column doesn't come into that of course - see Boeing vs AI FBW systems; but no doubt the French government saw the opportunity to get two for the price of one .....
CliveL