Future quantum communication will rely on the integration of single-photon sources, quantum memories and systems with strong single-photon nonlinearities. Two key parameters are crucial for the single-photon source: a high photon flux with a very small bandwidth, and a spectral match to other components of the system. Atoms or ions may act as single-photon sources--owing to their narrowband emission and their intrinsic spectral match to other atomic systems--and can serve as quantum nonlinear elements. Unfortunately, their emission rates are still limited, even for highly efficient cavity designs. Single solid-state emitters such as single organic dye molecules are significantly brighter and allow for narrowband photons; they have shown potential in a variety of quantum optical experiments but have yet to be interfaced with other components such as stationary memory qubits. Here we describe the optical interaction between Fourier-limited photons from a single organic molecule and atomic alkali vapours, which can constitute an efficient quantum memory. Single-photon emission rates reach up to several hundred thousand counts per second and show a high spectral brightness of 30,000 detectable photons per second per megahertz of bandwidth. The molecular emission is robust and we demonstrate perfect tuning to the spectral transitions of the sodium D line and efficient filtering, even for emitters at ambient conditions. In addition, we achieve storage of molecular photons originating from a single dibenzanthanthrene molecule in atomic sodium vapour. Given the large set of molecular emission lines matching to atomic transitions, our results enable the combination of almost ideal single-photon sources with various atomic vapours, such that experiments with giant single-photon nonlinearities, mediated, for example, by Rydberg atoms, become feasible.