Systematic studies of the ZrCuSiAs (also LaOAgS or 1111) structure type resulted in the synthesis of two new fluoride chalcogenides, EuFAgSe and EuFAg1-δTe, whereas their sulfide analog, EuFAgS, could not be obtained. Both new compounds are tetragonal, P4/nmm, with cell parameters a = 4.1542(1) Å, c = 9.2182(1) Å for the selenide and a = 4.3255(1) Å, c = 9.5486(1) Å for the telluride. Rietveld refinement reveals a significant silver deficiency in the telluride (δ = 0.05), while the selenide is nearly stoichiometric. Both compounds are semiconductors as shown by diffuse reflectance spectroscopy and confirmed by density-functional calculations of the band structure. Magnetism of both compounds is predominantly driven by Eu2+, as indicated by magnetic susceptibility measurements and corroborated by 151Eu Mössbauer spectroscopy. EuFAg1-δTe and EuFAgSe are paramagnetic down to 1.8 K.