In the Standard Model framework, lepton flavor is conserved in interactions. However, it can be violated in certain scenarios beyond the Standard Model. In this study, we consider (e tau) production through a four-Fermi lepton flavor violation interaction at the future electron-positron circular collider (FCC-ee). To constrain the Wilson coeffi- cients at four center-of-mass energies 157.5, 162.5, 240, and 365 GeV that have been proposed for the FCC-ee, a Standard Model Effective Field Theory (SMEFT) is used. The main sources of background are accounted for, and the study incorporates realistic de- tector effects. To enhance the results, we combine the individual constraints obtained at each center-of-mass energy. We show that the combined limits improve the sensitivity to lepton flavor violation couplings by a factor of approximately three compared to the individual results and are competitive with the Belle II prospects.