In these proceedings we study the scalar ($J^{PC}=0^{++}$, $S$) and tensor ($J^{PC}=2^{++}$, $T$) resonance contributions to the $\pi\pi\pi$ axial-vector form-factor (AFF), relevant for phenomenological studies of tau decays. Chiral symmetry and its isospin subgroup are key ingredients of our construction, implemented via a chiral invariant Lagrangian which incorporates $S$, $T$ and axial-vector ($A$) resonances and the light multiplet of pseudoscalars, the chiral Goldstones (pions, kaons and etas). Thus, one obtains the right isospin relation between the $\pi^0\pi^0\pi^-$ and $\pi^-\pi^-\pi^+$ production amplitudes. The chiral invariant construction ensures the recovery of the low-energy limit, provided by Chiral Perturbation Theory ($\chi$PT) and the transversality of the current in the chiral limit at all energies. The amplitudes are further constrained by imposing high-energy constraints, prescribed by Quantum Chromodynamics (QCD). We discuss the improvement of the Breit-Wigner and Flatt\'e representations for the broad $\sigma$ scalar resonance provided by the incorporation of the real logs required by analyticity, \`a la Gounaris-Sakurai. The aim of this work is to improve the description of these decay channels oriented to its implementation in the Tauola Monte Carlo and future Belle data analyses.