Smart surfaces that reversibly change the interfacial friction coefficients in response to external stimuli enable a wide range of applications, such as grips, seals, brake pads, packaging films, and fabrics. Here a new concept of such a smart frictional system is reported: a composite film of a plain-weave polyester textile sheet, and a thermo-responsive nematic liquid crystalline elastomer (LCE). The composite is deployed with retractable micro-undulations of the elastomer inside each weave mesh, enabling dramatic changes of the contact interface with the opposing surface on LCE actuation, which is induced e.g. by a change in temperature (T). At ambient T, the protruding viscoelastic parts of LCE in the nematic phase make contact with the opposing flat surface, resulting in a very high friction. At an elevated T (50C, isotropic phase), the undulations of LCE surface are retracted within the thickness of the textile, and the contacts are limited to small regions around overlapping textile fibers, lowering the friction dramatically. This effect is fully reversible on heating/cooling cycles. The surface undulations are spontaneous, i.e. fabricated without any lithographic or alignment techniques. The present composite opens a new way to practical uses of sheets/films with switchable friction enabled by stimuli-responsive LCEs.