We present the analysis of the inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconducting state in thin superconducting films in the parallel magnetic field. For the tetragonal crystal symmetry (relevant to CeCoIn₅ - the most probable candidate for the FFLO state formation) we predict a very peculiar in-plane angular dependence of the FFLO critical field due to the orbital effect. In the uniform superconducting state the critical field should be isotropic. The magnetic field pins also the direction of the FFLO modulation permitting thus to study the critical current anisotropy. Our calculations reveal a strong critical current anisotropy in the FFLO state in sharp contrast with the usual superconducting state. The predicted characteristic anisotropies of the critical field and critical current may provide an unambiguous probe of the FFLO phase formation.