expr1=F1[0]*F2[3]*F3[2]+4I*F1[1]*F2[2]*F3[1]-2*F1[0]*F2[-2]*F3[2]
expr2=4*F1[0]*F2[2]*F3[1]-I*F1[1]*F2[0]*F3[-1]-1*F1[1]*F2[0]*F3[2]+2*F1[6]*F2[1]*F3[1]

expr= c1*F1[z1]*F2[z2]*F3[z3]+c2*F1[z4]*F2[z5]*F3[z6]+c3*F1[z7]*F2[z8]*F3[z9] + ...

CoefficientList[expr, F2[__]*F3[__]*F4[__]]

exprnew = expr /. {F2[v2_] -> x^(2*v2), F3[v3_] -> x^(3*v3), F4[v4_] -> x^(5*v4)}
CoefficientList[exprnew, x]

CoefList[expr] -> {c1,c2,c3}
CoefList[expr1] -> {1,4I,-2}
CoefList[expr2] -> {4,-I,-1,+2}