In the framework of the protection of copper objects exposed to atmospheric corrosion, different solutions are envisaged, among them carboxylate treatments (HC$_{10}$). In this study, an analytical approach based on complementary techniques from micrometer to nanometer scale ($\mu$RS, SEM-EDS, SAM) is used to describe the properties of the corrosion products layer (CPL) and determine the penetration depth of the HC$_{10}$ protection treatment inside the CPL of copper samples issued from the roof of the Saint Martin church in Metz. The CPL consists in a thick brochantite layer (20 to 50 $\mu$m), mainly composed of Cu$_4$ SO$_4$ (OH)$_6$ , on top of a thinner (1 to 5 $\mu$m thick) cuprite layer, Cu$_2$O, acting as a natural corrosion barrier on the metal. Application of the organic treatment is implemented by immersing the corroded samples in HC$_{10}$ solution, consistent with future requirements for large scale applications. Even for short-term duration (one minute), the HC$_{10}$ treatment penetrates to the cuprite/brochantite interface, but Cu(C$_{10}$)$_2$ precipitate is only detected locally, whereas for a longer immersion of thirty minutes, it is present in higher proportions in the whole brochantite layer, filling the pores, up to the cuprite/brochantite interface. Cu(C$_{10}$)$_2$ acts as a second inner barrier and prevents liquid infiltration.