The Equivalence Principle is today challenged by some theories attempting to unify General Relativity and Quantum Mechanics. The MICROSCOPE mission thus intents to confirm or overturn this principle by testing the universality of free fall in space with an unrivaled precision objective of 10^-15. The principle of the test relies on the precise measurement of a gravitational signal by a differential electrostatic accelerometer (referred to as SAGE instrument) on board a drag-free microsatellite. The precision of the measurements exploited for the test is limited by several perturbations due to the high sensitivity of the instrument. The instrumental model implemented to process the collected data used overestimated models for some systematic errors such as the thermal sensitivity and coupling defects. The additional scientific measurements available by the end of the mission, will enable to perform a more in-depth exploration of these errors and thus to improve the current instrumental model. This is the purpose of this research work.