Context. The breakthrough developments of Cherenkov telescopes in the past decade have led to angular resolution of 0.1° and an unprecedented sensitivity. This has allowed the current generation of Cherenkov telescopes (H.E.S.S., MAGIC, and VERITAS) to discover a population of supernova remnants (SNRs) radiating in very-high-energy (VHE; E > 100 GeV) γ-rays. A number of those VHE SNRs exhibit a shell-type morphology that is spatially coincident with the shock front of the SNR.Aims. The members of this VHE shell SNR club are RX J1713.7−3946, RX J0852.0−4622, RCW 86, SN 1006, and HESS J1731−347. The last two objects have been poorly studied in high-energy (HE; 0.1 < E < 100 GeV) γ-rays and need to be investigated in order to draw the overall picture of this class of SNRs and to constrain the characteristics of the underlying population of accelerated particles.Methods. Using 6 years of Fermi-LAT P7 reprocessed data, we studied the GeV counterpart of the SNRs HESS J1731−347 and SN 1006. The two SNRs are not detected in the data set, and given that there is no hint of detection, we do not expect any detection in coming years from the SNRs. However in both cases, we derived upper limits that significantly constrain the γ-ray emission mechanism and can rule out a standard hadronic scenario with a confidence level >5σ.Results. With this Fermi analysis, we now have a complete view of the HE to VHE γ-ray emission of TeV shell SNRs. All five sources have a hard HE photon index (Γ < 1.8), which suggests a common scenario where the bulk of the emission is produced by accelerated electrons radiating from radio to VHE γ-rays through synchrotron and inverse Compton processes. In addition when correcting for the distance, all SNRs show a surprisingly similar γ-ray luminosity supporting the idea of a common emission mechanism. While the γ-ray emission is likely to be leptonic-dominated at the scale of the whole SNR, this does not rule out efficient hadron acceleration in those objects.Read less <