-Participant intended to receive SOC therapy per Investigator's judgment and local
        practice.
        Cohort A: Participants with chronic kidney disease who will receive a kidney transplant
        from a living or deceased donor to whom they are sensitized, and/or required
        desensitization prior to transplantation.
        Cohort B: Participants who are kidney transplant recipients diagnosed with active AMR.
          -  BMI ≤ 40 kg/m2.
          -  Contraceptive use by women during the treatment period, and for at least 49 weeks
             after the last administration of IMP (BIVV020 + SOC arm participant) or last treatment
             period visit (SOC arm participant).
          -  Contraceptive use by men during the treatment period, and for at least 49 weeks after
             the last administration of IMP (BIVV020 + SOC arm participant) or last treatment
             period visit (SOC arm participant).
          -  18-75 years old at the time of consent.
        Exclusion Criteria:
          -  Participants who are ABO incompatible with their donors.
          -  Participants with known active ongoing infection as per below:
               1. Positive HIV.
               2. Positive HBV.
               3. HCV with detectable HCV RNA.
               4. Within 4 weeks of first study intervention: any serious infection, or infection
                  requiring antibiotic treatment against an identified or suspected bacterial
                  pathogen.
          -  History of active tuberculosis (TB) regardless of treatment.
          -  Participants with clinical diagnosis of systemic lupus erythematosus (SLE).
          -  Prior treatment with complement system inhibitor within 5 times the half-life.
          -  Current enrollment in any other clinical study where the last investigational study
             treatment administration was within 5 half-lives from study intervention initiation.
        The above information is not intended to contain all considerations relevant to a patient's
        potential participation in a clinical trial.