We present de Haas-van Alphen (dHvA) measurements on an Eu-based valence-fluctuating system. EuIr2Si2 exhibits a temperature-dependent, noninteger europium valence with Eu2.8+ at low temperatures. The comparison of experimental results from our magnetic-Torque experiments in fields up to 32 T and density functional theory band-structure calculations with localized 4f electrons shows that the best agreement is reached for a Fermi surface based on a valence of Eu2.8+. The calculated quantum-oscillation frequencies for Eu3+ instead cannot explain all the experimentally observed frequencies. The effective masses, derived from the temperature dependence of the dHvA oscillation amplitudes, show not only a significant enhancement with masses up to 11me (me being the free electron mass), but also a magnetic-field dependence of the heaviest mass. We attribute the formation of these heavy masses to strong correlation effects resulting from valence fluctuations of 4f electrons being strongly hybridized with conduction electrons. The increase of the heavy masses with magnetic field likely results from the onset of the expected field-induced valence crossover that enhances these valence fluctuations but does not alter the Fermi-surface topology in the field range studied.