The influence of $^{57}\text{F}\text{e}$-doping and strain effects on the structural and magnetotransport properties of undoped and lightly doped $^{57}\text{F}\text{e}$ (1 and 3% at Mn site) ${\text{La}}_{2/3}{\text{Ca}}_{1/3}{\text{MnO}}_{3}$ thin films and bulk powder samples have been studied. Thin films were grown on $(100){\text{-SrTiO}}_{3}$ (STO) and $(100){\text{-LaAlO}}_{3}$ (LAO) single crystal substrates, via high ${\text{O}}_{2}$ pressure (500 mTorr) using dc magnetron sputtering. Conversion electron M\"ossbauer (CEM) spectra measured at room temperature in the paramagnetic regime of the Fe-doped samples do not show significant differences in the isomeric shift for the case of the ${\text{La}}_{2/3}{\text{Ca}}_{1/3}{\text{MnO}}_{3}$ films doped with 1 and 3% iron. The isomeric shift values correspond to the presence of Fe in the $3+$ state with octahedral coordination, thus indicating that Fe is incorporated into the structure by substituting Mn. The absence of further states in the spectra indicates that Fe is not involved in forming other additional impurity phases. The x-ray $\ensuremath{\theta}\text{\ensuremath{-}}2\ensuremath{\theta}$ scan showed that all thin films on LAO and STO have single phase and $c$-axis strong orientation along the growth direction and the Fe doping gives rise to a relaxation of the epitaxial strain. Finally, we have observed that the saturation magnetization, Curie temperature, metal-insulator transition, and magnetoresistance vary nonmonotonically with increased Fe concentration. This behavior can be understood in terms of competing influences from the strain relaxation, which enhances the tendency to order ferromagnetically, and the reduced double exchange, which is detrimental to the ferromagnetic order.