Concentrated solar power (CSP) has gained traction for generating electricity at high capacity and meeting base-load energy demands in the energy mix market in a cost-effective manner. The linear Fresnel reflector (LFR) is valued for its cost-effectiveness, reduced capital and operational expenses, and limited land impact compared to alternatives such as the parabolic trough collector (PTC). To this end, the aim of this study is to optimize the operational parameters, such as the solar multiple (SM), thermal energy storage (TES), and fossil fuel (FF) backup system, in LFR power plants using molten salt as a heat transfer fluid (HTF). A 50 MW LFR power plant in Duba, Saudi Arabia, serves as a case study, with a Direct Normal Irradiance (DNI) above 2500 kWh/m². About 600 SM-TES configurations are analyzed with the aim of minimizing the levelized cost of electricity (LCOE). The analysis shows that a solar-only plant can achieve a low LCOE of 11.92 ¢/kWh with a capacity factor (CF) up to 36%, generating around 131 GWh/y. By utilizing a TES system, the SM of 3.5 and a 15 h duration TES provides the optimum integration by increasing the annual energy generation (AEG) to 337 GWh, lowering the LCOE to 9.24 ¢/kWh, and boosting the CF to 86%. The techno-economic optimization reveals the superiority of the LFR with substantial TES over solar-only systems, exhibiting a 300% increase in annual energy output and a 20% reduction in LCOE. Additionally, employing the FF backup system at 64% of the turbine’s rated capacity boosts AEG by 17%, accompanied by a 5% LCOE reduction. However, this enhancement comes with a trade-off, involving burning a substantial amount of natural gas (503,429 MMBtu), leading to greenhouse gas emissions totaling 14,185 tonnes CO₂ eq. This comprehensive analysis is a first-of-a-kind study and provides insights into the optimal designs of LFR power plants and addresses thermal, economic, and environmental considerations of utilizing molten salt with a large TES system as well as employing natural gas backup. The outcomes of the research address a wide audience including academics, operators, and policy makers.