The investigators propose a phase II study to evaluate the efficacy of carboplatin monotherapy in the tumor subgroup of metastatic castration-resistant prostatic carcinomas with somatic abnormality in the Homologous Recombination (HR) pathway.

This study may also better characterize the molecular abnormalities of tumors required for the carboplatin response

Inclusion Criteria:

• Patients > 18 years old

• Patients with adenocarcinoma or poorly differentiated prostate carcinoma, histologically confirmed (small-cell histology or high-grade neuroendocrine histology excluded)

• Tumor presenting a somatic pathogenic variant likely to alter the homologous recombination pathway previously detected on a tumor biopsy or on circulating tumor DNA, or germinal mutation among the list of genes defined in the study

• Castration-resistant tumor defined by progression despite well-conducted androgen deprivation treatment: testosterone ≤50ng /dL agonist / antagonist of luteinizing hormone-releasing hormone (LHRH) or surgical castration. The patient must agree to continue concomitant LHRH-mediated (agonist or antagonist) therapy throughout the duration of the study regimen for patients with no history of surgical castration.

• Patients must have performed at least one line of chemotherapy by taxane in case of castration resistance:

  • Patients who have received docetaxel treatment in a hormone-sensitive situation must have received at least treatment with cabazitaxel in case of castration resistance
  • Patients who have not received chemotherapy in a hormone-sensitive situation must have received docetaxel AND cabazitaxel or have a contraindication to discontinue treatment.

• Patients must have been treated with at least 2nd generation hormone therapy (eg, abiraterone acetate or enzalutamide)

• Patients may have been treated with a poly (ADP-ribose) polymerase inhibitor (PARP)

• Performance Status <2

• Metastatic disease progressive

Exclusion Criteria:

• Absence of previous treatment with taxane in situation of sensitivity or resistance to castration.
• Absence of previous treatment with cabazitaxel in case of resistance to castration (except contraindication explaining the non-administration of treatment)
• No treatment with 2nd generation hormone therapy (eg abiraterone acetate or enzalutamide) unless contraindicated to explain non-administration of treatment
• Previous treatment with platinum
• Symptomatic and untreated central nervous system (CNS) metastases. Patients with asymptomatic and pre-treated CNS metastases are included if they are clinically stable (not requiring corticosteroid therapy for 28 days) and must have a brain MRI evaluation at screening and during follow-up.