Efficacy of a Maintenance Treatment With TALAzoparib Following First Line Platinum-based Chemotherapy in Malignant MESOthelioma

Inclusion Criteria: * Patients older than 18 years old * Patients with Eastern Cooperative Oncology Group (ECOG) performance status ≤2 * Histologically - or cytologically - confirmed malignant mesotheliomas: epithelioid, sarcomatoid, biphasic * Developed from pleura (cohort A) or from peritoneum (cohorts B1 and B2) * Previously treated with first-line platinum based-chemotherapy (including minimum one cycle of pemetrexed) for 4 to 6 cycles, with no sign of disease progression during chemotherapy. * No previous treatment with bevacizumab and PARP inhibitor * Minimum 6 weeks and maximum 8 weeks interval between last chemotherapy cycle and talazoparib start * For pleural mesotheliomas (cohort A), primary or interval debulking surgery with or without hyperthermic intrapleural or intrathoracic chemotherapy (HITHOC) will be authorized, in the case of non-complete cytoreductive surgery only * For peritoneal mesotheliomas * In cohort B1, primary or interval debulking surgery ± hyperthermic intraperitoneal chemotherapy (HIPEC) will be authorized in the case of non-complete cytoreductive surgery (CC2 or CC3) only. This cohort will also include patients with non-operated diseases * In cohort B2, complete macroscopic (CC0 or CC1) primary or interval debulking surgery ± HIPEC will be required. Intraperitoneal treatment with pressurized intraperitoneal aerosol chemotherapy sessions (PIPAC) are not allowed. * Measurable or non-measurable (but radiologically evaluable) disease as per modified RECIST version 1.1 on computed tomography (CT) scan (within 28 days of talazoparib initiation) * Availability at the study site of a representative FFPE tumor sample in a block or at least 30 unstained slides from biopsy or surgery specimen, aged less than 6 months. * Patients with adequate bone marrow function measured within 28 days prior to administration of study treatment as defined below: * Absolute neutrophil count ≥1.0 x 109 /L * Platelet count ≥50 x 109 /L * Haemoglobin ≥8.0 g/dL (may have been blood transfused) * Patients with adequate renal function: * Calculated Glomerular Filtration Rate (GFR) ≥30 ml/min/1.73 m2 according to CKD-EPI formula * Patients with adequate hepatic function * Total bilirubin ≤ 1 × upper limit of normal \[ULN\] and aspartate aminotransferase (AST) \> ULN * Total bilirubin \> 1.0 to1.5 × ULN and any AST * Patients must have a life expectancy ≥16 week. * Confirmation of non-childbearing status (pregnancy test) for women of childbearing potential. * A highly effective method of contraception is required for female patients during treatment of talazoparib, and for at least 7 months after completing therapy. Advise male patients with female partners of reproductive potential and pregnant partners to use a condom, during treatment with talazoparib and for at least 4 months after the final dose. * Patients who gave its written informed consent to participate to the study. * Patients affiliated to a social insurance regime. * Patients are willing and able to comply with the protocol for the duration of the study including undergoing treatment and scheduled visits and examinations including follow up. Exclusion Criteria: * Uncontrolled intercurrent illness, including but not limited to, such as congestive heart failure; respiratory distress; liver failure; allergy, or psychiatric illness/social situations that would limit compliance with study requirement according to the investigator, substantially increase risk of incurring AEs or compromise the ability of the patient to give written informed consent. * Patients with second primary cancer, except: adequately treated non-melanoma skin cancer, curatively treated in-situ cancer of the cervix, or other solid tumours curatively treated with no evidence of disease for ≥5 years. * All subjects with brain metastases or meningeal involvement. * Patients receiving any systemic chemotherapy, radiotherapy (except for palliative reasons), within 6 weeks from the last dose prior to study treatment (or a longer period depending on the defined characteristics of the agents used). The patient can receive a stable dose of bisphosphonates for bone metastases, before and during the study as long as these were started at least 4 weeks prior to treatment with study drug. * Persistent toxicities (CTCAE ≥grade 2) with the exception of alopecia and sensory neuropathy, caused by previous cancer therapy. * Treatment with other investigational agents. * Bowel occlusive syndrome, inflammatory bowel disease, immune colitis, or other gastro-intestinal disorder that does not allow oral medication such as malabsorption. * Known severe hypersensitivity reactions to PARP inhibitors. * Known HIV or AIDS related illness. * Positive test for HBV surface antigen and / or confirmatory HCV RNA (if anti-HCV antibody tested positive). * Treatment with oral anticoagulant anti-vitamin K such Coumadin® * Prior organ transplantation, including allogeneic stem cell transplantation (excluding autologous bone marrow transplant). * Patients under guardianship. * Women who are breastfeeding (during treatment with talazoparib and for at least 1 month after the final dose) * Participation in other interventional clinical research that may interfere with the experimental drugs efficacy.