  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 CeCoIn$_{5}$ -
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.
