Temperature- and fluence-dependent carrier dynamics of the magnetic kagome metal Fe₃Sn₂ were studied using the ultrafast optical pump-probe technique. Two carrier relaxation processes and a laser-induced coherent optical phonon were observed. We ascribe the shorter relaxation (~1 ps) to hot electrons transferring their energy to the crystal lattice via electron–phonon scattering. The second relaxation (~30 ps), on the other hand, cannot be explained as a conventional process, and we attributed it to the unconventional (localized) carriers in the material. The observed coherent oscillation is assigned to be a totally symmetric A_1g optical phonon dominated by Sn displacements out of the kagome planes and possesses a prominently large amplitude, on the order of 10⁻³, comparable to the maximum of the reflectivity change (ΔR/R). This amplitude is similar to what has been observed for coherent phonons in charge-density-wave (CDW) systems, although no signs of such instability were hitherto reported in Fe₃Sn₂. Our results suggest an unexpected connection between Fe₃Sn₂ and kagome metals with CDW instabilities and a strong interplay between phonon and electron dynamics in this compound.