  The Weak Equivalence Principle (WEP) and the local Lorentz invariance (LLI)
are two major assumptions of General Relativity (GR). The MICROSCOPE mission,
currently operating, will perform a test of the WEP with a precision of
$10^{-15}$. The data will also be analysed at SYRTE for the purposes of a LLI
test realised in collaboration with J. Tasson (Carleton College, Minnesota) and
Q. Bailey (Embry-Riddle Aeronautical University, Arizona). This study will be
performed in a general framework, called the Standard Model Extension (SME),
describing Lorentz violations that could appear at Planck scale ($10^{19}$
GeV). The SME allows us to derive a Lorentz violating observable designed for
the MICROSCOPE experiment and to search for possible deviations from LLI in the
differential acceleration of the test masses.
