The magnetic phase transition in the invar Fe₆₅Ni₃₅ alloy has been investigated by small-angle polarized-neutron scattering (SAPNS) along with both three-dimensional neutron depolarization and thermal-expansion measurements. The data give evidence for a smeared phase transition. A spatial distribution in the Curie temperature T_C is introduced to explain the experimental data. The local T_C variations are described by the standard deviation of the transition temperature ΔT_C and by the characteristic length of the T_C variations, R₀. The deduced parameters are (T_C) = 485 ± 0.5 K, ΔT _C = 12.5 ± 0.2 K, and R₀≈300 nm. The critical SAPNS experiment was performed in a special inclined geometry (H ^→ is inclined to the wave vector k^→). Two different contributions to the critical scattering were analyzed in the magnetic-field range (1-1000 G) and the temperature range (T_C ± 0.1T_C) of interest. First, the two-spin-correlation function was studied. Second, the dynamical three-spin-correlation function, or the so-called dynamical chirality of the system, was investigated by extracting the asymmetric part of the polarization-dependent scattering. We distinguish two contributions in the chiral scattering, which stem from the spin waves in the large magnetic inhomogeneities and from the three-spin-correlation function of the critical fluctuations. The data are interpreted in terms of the static and dynamic scaling theory accounting for the concept of local T_C variations.