To achieve an aerodynamically efficient design of fuselage for bioinspired unmanned aerial vehicles (UAV), the development of a systematic method is of paramount need. This work presents a multiobjective optimization study for shape parameterization of a 2D fuselage of foldable flapping wing UAV in low Reynolds number (2e05) flight conditions. The novelty of the research work lies in integrating S1223 airfoil characteristics for predicting the efficient shape design of the fuselage. This paper offers four sections; (i) the validation of the ANSYS Fluent model with experiment, (ii) the exploration of design variables using Design of Experiment (Sparse Grid Initialization), (iii) the implementation of response surface method (Genetic Aggregation) to know about dimensional sensitivity among independent and dependent variables and (iv) the application of multiobjective optimization method i.e. NSGA II to optimize the drag and lift coefficient. To identify the superiority, a comparative study between the original and optimized fuselage is presented considering many parameters like pressure contours, velocity contours, pressure coefficients, and streamlines representations. It is evident from various results that the 2D optimum shape significantly minimizes the drag coefficient and increases the lift coefficient. This work also makes room for 3D shape optimization, which helps in prototype fabrication for real-time flight conditions.