  Ultrathin FeSe films grown on SrTiO$_{3}$ substrates are a recent milestone
in atomic material engineering due to their important role in understanding
unconventional superconductivity in Fe-based materials. Using femtosecond time-
and angle-resolved photoelectron spectroscopy, we study phonon frequencies in
ultrathin FeSe/SrTiO$_{3}$ films grown by molecular beam epitaxy. After optical
excitation, we observe periodic modulations of the photoelectron spectrum as a
function of pump-probe delay for 1 unit cell, 3 unit cell, and 60 unit cell
thick FeSe films. The frequencies of the coherent intensity oscillations
increase from 5.00(2) to 5.25(2) THz with increasing film thickness. By
comparing with previous works, we attribute this mode to the Se A$_\textrm{1g}$
phonon. The dominant mechanism for the phonon softening in 1 unit cell thick
FeSe films is a substrate-induced lattice strain. Our results demonstrate an
abrupt phonon renormalization due to a lattice mismatch between the ultrathin
film and the substrate.
