TE Flaps were converted to all electronic control on the -400 and the Stab Trim was all electric (no manual stab trim levers in the cockpit).
"Fly by wire" usually refers to primary flight controls -- ailerons, elevators, and rudder. In this regime, the 744 is strictly conventional.
While control of TE flaps may be electric/electronic, actuation is still by hydraulics, and there is NO automatic adjustment of LE or TE flaps (as in the F/A-18 and other "fly by wire" aircraft).
The bottom line is that by any conventional measure, the 744 is NOT a "fly by wire" airplane.