Using Monte Carlo simulations of a coarse grained lattice model, we study conformations and concentration fluctuations of polymers confined into thin films. We vary the chain length from N=32 to 512. As we reduce the film thickness to the unperturbed radius of gyration R-g, the chain extension parallel to the surface increase only by about 5% for the largest chain length. Confinement has, however, a much more pronounced effect on intra- and intermolecular correlations: the surfaces make the chain fold back into the volume it occupies and squeeze out neighboring chains. Decreasing the film thickness, we reduce the interdigitation of chains. This gives rise to deviations from the ideal Gaussian chain structure for wave vectors qR(g)>1, which are qualitatively similar to corrections observed in semidilute (bulk) solutions. Fitting the structure factor with a Debye function in this Kratky regime, we systematically overestimate the chain extension by up to 15%. Additional (minor) deviations from the incompressible random phase approximation at large wave vectors are found. As we reduce the film thickness the correlation function of the centers of mass develops a very strong correlation hole and resembles in thin films that of a two-dimensional fluid of soft particles.