Debris discs around main-sequence stars are belts of planetesimals - asteroids and comets - formed in the protoplanetary discs around young stars. Planetesimals comprise both the building blocks of planets around young stars and the source of dusty debris around older stars. Imaging observations of dust continuum emission and scattered light reveal the location of these planetesimal belts around their host stars. Analysis of debris discs observed at millimetre wavelengths revealed a trend between the discs' radii and the host star luminosities. This trend was tentatively linked to the preferential formation of dust-producing planetesimals near snow lines (specifically CO) in the protoplanetary discs around the host stars. Here, we perform a homogeneous analysis of 95 debris discs observed at far-infrared wavelengths by the Herschel Space Observatory and fit the obtained distribution of radii and widths as a function of stellar luminosity with a power-law relation. We identify a trend in disc radius as a function of stellar luminosity similar to that identified at millimetre wavelengths, but cannot convincingly recover it from the available data set due to the large uncertainties on disc radius and width inherent in the marginally spatially resolved data, and the bias of smaller discs around more distant stars (which are also the more luminous) being omitted from our analysis. We see a trend in disc temperature as a function of stellar luminosity, consistent with previous findings from similar analyses.