  Owing to both electronic and dielectric confinement effects, two-dimensional
organic-inorganic hybrid perovskites sustain strongly bound excitons at room
temperature. Here, we demonstrate that there are non-negligible contributions
to the excitonic correlations that are specific to the lattice structure and
its polar fluctuations, both of which are controlled via the chemical nature of
the organic counter-cation. We present a phenomenological, yet quantitative
framework to simulate excitonic absorption lineshapes in single-layer
organic-inorganic hybrid perovskites, based on the two-dimensional Wannier
formalism. We include four distinct excitonic states separated by
$35\pm5$\,meV, and additional vibronic progressions. Intriguingly, the
associated Huang-Rhys factors and the relevant phonon energies show substantial
variation with temperature and the nature of the organic cation. This points to
the hybrid nature of the lineshape, with a form well described by a Wannier
formalism, but with signatures of strong coupling to localized vibrations, and
polaronic effects perceived through excitonic correlations. Our work highlights
the complexity of excitonic properties in this class of nanostructured
materials.
