The isovector charge and anomalous magnetic moment form factors of the nucleon are calculated assuming that the low-energy part of the spectral function is determined by the two-pion intermediate state and the high-energy part of the spectral function can be represented by a subtraction constant. The results are compared with experimental analysis in the form of a pole plus a subtraction constant for each form factor. The spectral function is given in terms of the pion form factor ($2\ensuremath{\pi}\ensuremath{\rightarrow}\ensuremath{\gamma}$) and the $N\overline{N}\ensuremath{\rightarrow}2\ensuremath{\pi}$ amplitudes. The phase of $2\ensuremath{\pi}\ensuremath{\rightarrow}\ensuremath{\gamma}$ as well as $N\overline{N}\ensuremath{\rightarrow}2\ensuremath{\pi}$ are determined in terms of $\ensuremath{\pi}\ensuremath{\pi}$ $p$-wave phase shift which is adjusted to fit the observed $\ensuremath{\rho}$-resonance with a mass of 760 MeV and a full width of \ensuremath{\sim}130 MeV. In the calculation of the $N\overline{N}\ensuremath{\rightarrow}2\ensuremath{\pi}$ amplitudes, the exchange of a nucleon and a (3-3) resonance are included as Regge poles. Two parameters are introduced in the Regge pole description. These parameters are adjusted to fit two constants ${a}_{1}$ and ${a}_{2}$ obtained from the experimental analysis of the form factors. The effective mass of the two-pion state which results from the present calculation is approximately 600 to 650 MeV (well below the $\ensuremath{\rho}$ mass), in good agreement with the experimental determination.