  The origin of the high-temperature superconducting state observed in FeSe
thin films, whose phase diagram displays no sign of magnetic order, remains a
hotly debated topic. Here we investigate whether fluctuations arising due to
the proximity to a nematic phase, which is observed in the phase diagram of
this material, can promote superconductivity. We find that nematic fluctuations
alone promote a highly degenerate pairing state, in which both $s$-wave and
$d$-wave symmetries are equally favored, and $T_{c}$ is consequently
suppressed. However, the presence of a sizable spin-orbit coupling or inversion
symmetry-breaking at the film interface lifts this harmful degeneracy and
selects the $s$-wave state, in agreement with recent experimental proposals.
The resulting gap function displays a weak anisotropy, which agrees with
experiments in monolayer FeSe and intercalated Li$_{1-x}$(OH)$_{x}$FeSe.
