Very-high-energy (VHE, E > 100 GeV) gamma radiation has already been detected from several supernova remnants (SNRs). These objects, which are well-studied in radio, optical and X-ray wavelengths, constitute one of the most intriguing source classes in VHE astronomy. H.E.S.S., an array of four imaging atmospheric Cherenkov telescopes in Namibia, has recorded an extensive dataset of VHE gamma-ray observations covering the central region of the Milky Way, both from pointed observations as well as from the Galactic Plane Survey conducted in the inner region of the Galaxy. From radio observations, several hundred SNRs are known in the Milky Way, but until now only few of them have been identified as VHE gamma-ray emitters. Using the H.E.S.S. dataset and a large ensemble of radio SNRs localized in the inner region of the Galaxy, the standard framework that links the origin of cosmic rays to the gamma-ray visibility of SNRs can now be tested. Here we present the ensemble of investigated SNRs and discuss constraints on the parameter space used within a theoretical model of hadronic VHE gamma-ray production.