Fe$_{1-x}$Crx thin films on Si and fused-SiO2 substrates were prepared using ion-beam sputtering deposition. Films with x = 0.69 and x = 0.49 were characterised by X-ray diffraction and conversion electron Mössbauer spectroscopy experiments, and concurrently the elastic and plastic behaviours were investigated through indentation tests. For x = 0.69, the paramagnetic bcc structure is observed, while the indentation modulus and hardness values are found to be 160 and 8.7 GPa, respectively. For x = 0.49, a strongly $\langle 200\rangle$-textured paramagnetic phase is evidenced, having the A15 structure. Mössbauer measurements also allowed the site occupancy to be determined. The structural change from bcc to A15 phase yields a 50% increase in hardness, while the indentation modulus remains unchanged. This particular behaviour is discussed in terms of distances between near neighbours and Burgers vector length in both bcc and A15 structures. The results obtained here provide motivation to pursue the present study through wear experiments.