Keratin fibre treatment process using a particular divalent or trivalent fatty acid salt and composition comprising said salt

A process for treating keratin fibres, comprising step i) or step i′) below:

• i) application to the keratin fibres of a composition (A) at acidic pH, composition A comprising a) one or more divalent or trivalent salts of fatty acids chosen from the compounds of formula (I) below, isomers thereof, solvates thereof, hydrates thereof, or mixtures thereof:
• in which formula (I):
• R represents a linear or branched, saturated or unsaturated hydrocarbon-based group comprising from 7 to 29 carbon atoms, the hydrocarbon-based group being optionally substituted with one or more identical or different groups chosen from:
• —COO− or —OH;
• X represents an alkaline-earth metal, a transition metal, a post-transition metal or a lanthanide;
• m represents a stoichiometric coefficient chosen so as to ensure the electrical neutrality of the compound of formula (I);
• n denotes an integer equal to 2 or 3;
• i′) applying to the keratin fibres a composition (B) at acidic pH, composition B comprising:
• a′) one or more fatty acids chosen from the compounds of formula (II) below, isomers thereof, solvates thereof, hydrates thereof, or mixtures thereof:
• in which formula (II) R1 represents a linear or branched, saturated or unsaturated hydrocarbon-based group comprising from 7 to 29 carbon atoms, the hydrocarbon-based group being optionally substituted with one or more identical or different groups chosen from:
• —COOH− or —OH;
• and
• b′) one or more metal salts chosen from mineral or organic salts of alkaline-earth metals, transition metals, post-transition metals, lanthanides, solvates of these salts, hydrates thereof, or mixtures thereof.