Recently, we reported the synthesis and investigations of EuSr2Bi2S4F4 and Eu2SrBi2S4F4. We have now been able to induce superconductivity in EuSr2Bi2S4F4 by Se substitution at the S site (isovalent substitution) with Tc = 2.9 K in EuSr2Bi2S2Se2F4. The other compound, Eu2SrBi2S4F4, shows a significant enhancement of Tc. In Se-substituted Eu2SrBi2S4-xSexF4, we find Tc = 2.6 K for x = 1.5 and Tc = 2.8 K for x = 2, whereas Tc = 0.4 K in the Se-free sample. In addition to superconductivity, an important effect associated with Se substitution is that it gives rise to remarkable changes in the Eu valence. Our 151Eu Mössbauer and X-ray photoemission spectroscopic measurements show that Se substitution in both of the compounds Eu2SrBi2S4F4 and EuSr2Bi2S4F4 gives rise to an increase in the Eu2+ component in the mixed-valence state of Eu.