We demonstrate in-line phase-contrast imaging of nanothickness foils by using a relatively large, polychromatic, debris-free femtosecond-laser-driven cluster-based plasma soft x-ray source, and a high-resolution, large dynamic range LiF crystal detector. The spatial coherence length of radiation in our setup reached a value of 5 microm on the sample plane, which is enough to observe phase-contrast enhancement in the images registered by the detector placed only a few hundred micrometers behind the object. We have developed a tabletop soft x-ray emission source, which emits radiation within a 4pi sr solid angle, and which allows one to obtain contact and propagation-based phase-contrast imaging of nanostructures with 700 nm spatial resolutions. This advance could be of utility for metrology applications.