Planetary nebulae (PNe) are the only single stars in galaxies outside the Local Group that can be used as kinematic tracers of the diffuse light in the extended halo. Analysing their luminosity-specific number density across galaxies of different morphologies has also shown hints that they may be used as tracers of the age and metallicity of stellar populations. A proper understanding of this relation has been hindered by the fact that simultaneously detecting PNe and accurately measuring stellar properties is extremely difficult using classical narrow-band imaging methods, which cannot detect PNe in the bright centres of galaxies. In this work, we use integral-field spectroscopy to overcome this challenge, analysing the inner regions of a sample of 10 early-type galaxies from the Extended Planetary Nebulae Survey (ePN.S) for which archival MUSE data were available. With the Diffuse Emission-Line Filter (DELF) technique, we automate the detection of PNe, and perform spectral fitting on the diffuse light to infer kinematics and stellar population parameters. We compare the PN number density profile and its associated α-parameter with multiple properties of the host galaxies. We find that our sample follows the previously observationally constrained correlation with the metallicity of the host galaxy. We find a weak anticorrelation between the α-parameter and the far-ultraviolet excess, highlighting the possible relation between the visibility lifetime of PNe on the spectral energy distribution of their host galaxies, with fewer PNe detected in association with stellar populations characterized by an ultraviolet excess.