We characterize the fluctuation properties of a polymer chain under external tension and the fluctuation-induced forces between two ring molecules threaded around the chain. The problem is relevant in the context of fluctuation-induced forces in soft-matter systems, features of liquid interfaces, and to describe the properties of polyrotaxanes and slide-ring materials. We perform molecular-dynamics simulations of the Kremer-Grest bead-spring model for the polymer and a simple ring-molecule model in the canonical ensemble. We study transverse fluctuations of the stretched chain as a function of chain stretching and in the presence of ring-shaped threaded molecules. The fluctuation spectra of the chains are analyzed in equilibrium at constant temperature, and the differences in the presence of two-ring molecules are compared. For the rings located at fixed distances, we find an attractive fluctuation-induced force between the rings, proportional to the temperature and decaying with the ring distance. We characterize this force as a function of ring distance, chain stretching, and ring radius, and we measure the differences between the free chain spectrum and the fluctuations of the chain constrained by the rings. We also compare the dependence and range of the force found in the simulations with theoretical models coming from different fields.