The future TESSERACT experiment will search for individual galactic DM particles below the proton mass through interactions with advanced, ultra-sensitive detectors. Currently TESSERACT is in a design phase aiming to produce fully defined detector technologies that will explore DM masses down to 10 MeV. It is designed to be sensitive to DM candidates interacting with the detector target material in producing both nuclear recoil DM (NRDM) and electron recoil (ERDM). To do so, multiple target materials will be used with varying detection strategies to ensure the capability to both actively reject the so-called low-energy excess and discriminate nuclear recoils against electron recoils. In addition to maximizing sensitivity to a variety of DM interactions, this provides an independent handle on instrumental backgrounds. Nowadays, the TESSERACT project encompasses two US-based technologies, namely HeRALD using superfluid helium as a target material, and SPICE using polar crystals (Al$_{2}$O$_{3}$ and SiO$_{2}$) and scintillating crystals such as GaAs. In these proceedings, we discuss the recent proposal to host the future TESSERACT experiment at the Modane Underground Laboratory (LSM) and add a third French-based cryogenic semiconducting (Ge, Si) detector technology to the TESSERACT payload.