In Europe, the DEMO test facility for Breeding Blankets (BB) will be the next step for fusion energy after ITER. The BB is a key component facing the plasma and ensuring tritium self-sufficiency, shielding against neutrons and heat extraction for electricity production. Within the EU research program, the two concepts candidates as driver BB in DEMO consider high-pressure coolants (water or helium) and Lithium-Lead or Beryllium pebble beds as breeder. In this article, an advanced BB concept is propounded as a candidate to be tested in DEMO taking into account Molten Salt (MS) as breeder and coolant and, consequently, named Breeder and Coolant Molten Salt (BCMS) BB. BCMS BB have several advantages, which lead to their investigations. As the MS is not pressurized during operation, high requirements associated to Nuclear Pressure Equipment (ESPN / PED) could be relaxed. Furthermore, the MS magnetohydrodynamic (MHD) flow is low due to its weak electrical conductivity. Besides, MS BB have identified drawbacks such as the structural material compatibility and the MS chemistry control needed during irradiation. A bibliographic review of MS and compatible materials is conducted. Promising BCMS BB are analysed regarding the Tritium Breeding Ratio (TBR) to test the capability of such MS breeders to reach the targeted TBR. The main nuclear quantities are evaluated with various MS on a dedicated model via the TRIPOLI-4® Monte-Carlo code: TBR, nuclear heating, neutron flux, displacement damage and helium production are reported and discussed. Moreover, the thermal and thermo-hydraulic responses of the MS BB are evaluated regarding the pressure drops (ΔP), the Pumping Power (PP) and the maximum temperatures in the structures. Nonetheless, preliminary design options are investigated. Finally, the major purpose is to evaluate the feasibility of a BCMS BB and identify their advantages and drawbacks.