This paper considers the downlink of an ultra-reliable low-latency communication (URLLC) system in which a base station (BS) serves multiple single-antenna users in the short (finite) blocklength (FBL) regime with the assistance of a reconfigurable intelligent surface (RIS). In the FBL regime, the users' achievable rates are complex functions of the beamforming vectors and of the RIS's programmable reflecting elements (PREs). We propose the joint design of the transmit beamformers and PREs, the problem of maximizing the geometric mean (GM) of these rates (GM-rate) and show that this aforementioned results are providing fair rate distribution and thus reliable links to all users. A novel computational algorithm is developed, which is based on closed forms to generate improved feasible points, using its execution. The simulations show the merit of our solution.