You're method seems sound but the answer you have is too low. Conversion of TAS from kts to m/s perhaps? I ran through it and got Cl = 0.3 ish.
As a first approximation, CL = Cl_alfa * AoA, where Cl_alfa is a constant dependent on aerofoil and wing geometry. Good luck finding any accurate numbers for the A320, but I think Cl_alfa = 5-6 rad^-1 is the rough range.
As others have pointed out, this method gives the effective "whole aircraft" Cl. To get the Cl for the wing in isolation and a true AoA much more detail regarding the tailplane, fuselage lift contribution etc etc would be needed. As a rough approximation though it shouldn't be too far out.