Lepton flavor violating interactions are absent in the standard model but are expected in various beyond-standard models. In this work, the potential of the future circular electron-positron collider to probe the four-fermion lepton flavor couplings via the e+e-→e±τ∓ process is revisited by means of an effective field theory approach. We provide constraints at 95% C.L. on the dimension-six Wilson coefficients including major sources of background processes and considering realistic detector effects at four expected operation energies, s=157.5, 162.5, 240, and 365 GeV, according to their corresponding integrated luminosities. We demonstrate that the statistical combination of the results from four center-of-mass energies improves the sensitivity to the lepton flavor violation couplings significantly. We compare the results with the prospects from the Belle II Collaboration with 50 ab-1 and other studies at electron-positron colliders.