In the Molten Salt Reactor (MSR), nuclear fuel dissolves directly into the coolant, thereby leading to an immediate release of fission products. Regular extraction of these fission products from the coolant is crucial to maintaining the reactor's performance efficiency, safety, and to facilitate more efficient waste storage and disposal procedures. Similarly, an accumulation of fission products within a molten salt bath during the electrorefining stage of pyroprocessing significantly impedes the efficiency of the separation process. Thus, it is necessary to remove these fission products at optimal intervals to preserve the integrity of the bath and reduce the generation of excessive nuclear waste. To manage these challenges effectively, real-time monitoring of the fission product concentrations in the molten salt is required. In this study, we have proposed the use of Laser-Induced Breakdown Spectroscopy (LIBS) to monitor and measure the concentrations of fission products such as strontium (Sr) and barium (Ba) in a LiCl-KCl eutectic at 823K. We obtained LIBS spectra from LiCl-KCl samples, which contained individual elements spanning a wide concentration range. Subsequently, we calculated the limits of detection and maximum detectable concentrations for Sr and Ba using highly accurate calibration curves. In addition to performing a univariate analysis, we also applied Partial Least Squares Regression (PLSR) to the data to establish superior calibration models for a more precise quantitative analysis. This was achieved by using the LIBS data measured when Sr and Ba were simultaneously dissolved in the molten salt. Consequently, we obtained low values for both Root Mean Square Error of Calibration (RMSEC) and Root Mean Square Error of Cross-Validation (RMSECV).