The use of numerical simulations to design and optimize turbine vane cooling requires precise prediction of the fluid mechanics and film cooling effectiveness. This results in the need to numerically identify and assess the various origins of the losses taking place in such systems and if possible in engine representative conditions. Large-Eddy Simulation (LES) has shown recently its ability to predict turbomachinery flows in well mastered academic cases such as compressor or turbine cascades. When it comes to industrial representative configurations, the geometrical complexities, high Reynolds and Mach numbers as well as boundary condition setup lead to an important increase of CPU cost of the simulations. To evaluate the capacity of LES to predict film cooling effectiveness as well as to investigate the loss generation mechanisms in a turbine vane in engine representative conditions, a wall-modeled LES of the FACTOR film-cooled nozzle is performed. After the comparison of integrated values to validate the operating point of the vanes, the mean flow structure is investigated. In the coolant film, a strong turbulent mixing process between coolant and hot flows is observed. As a result, the spatial distribution of time-averaged vane surface temperature is highly heterogeneous. Comparisons with the experiment show that the LES prediction fairly reproduces the spatial distribution of the adiabatic film effectiveness. The loss generation in the configuration is then investigated. To do so, two methodologies, i.e, performing balance of total pressure in the vanes wakes as mainly used in the literature and Second Law Analysis (SLA) are evaluated. Balance of total pressure without the contribution of thermal effects only highlights the losses generated by the wakes and secondary flows. To overcome this limitation, SLA is adopted by investigating loss maps. Thanks to this approach, mixing losses are shown to dominate in the coolant film while aerodynamic losses dominate in the coolant pipe region.