  We investigate the vector and axial-vector form factors for the pion
radiative weak decays $\pi^+\to e^+\nu_e \gamma$ and $\pi^+\to e^+\nu_e e^+
e^-$, based on the gauged effective chiral action from the instanton vacuum in
the large $N_c$ limit. The nonlocal contributions, which arise from the gauging
of the action, enhance the vector form factor by about $20\,\%$, whereas the
axial-vector form factor is reduced by almost $30\,\%$. Both the results for
the vector and axial-vector form factors at the zero momentum transfer are in
good agreement with the experimental data. The dependence of the form factors
on the momentum transfer is also studied. The slope parameters are computed and
compared with other works.
