Avelumab in Chemo-resistant Gestational Trophoblastic Neoplasias

Inclusion criteria for all patients : * Woman older than 18 years - Patients with Eastern Cooperative Oncology Group (ECOG) performance status ≤ 2 * Patients with adequate bone marrow function : * Absolute neutrophil granulocyte count ≥ 1.5 x 10 9 /L * Platelet count ≥ 100 x 10 9 /L * Haemoglobin ≥ 9.0 g/dL (may have been blood transfused). * Patients with adequate renal function : * Calculated creatinine clearance \>= 30 ml/min according to the Cockcroft-Gault formula (or local institutional standard method) * Patients with adequate hepatic function * Serum bilirubin ≤ 1.5 x UNL and AST/ALT ≤ 2.5 X UNL (≤ 5 X UNL for patients with liver metastases) * Patients must have a life expectancy ≥ 16 weeks * Confirmation of non-childbearing status for women of childbearing potential. An evolutive pregnancy can be ruled out in the following cases: * in case of a previous hysterectomy * if serum hCG level ≥ 2 000 IU/L and no intra or extra-uterine gestational sac is detected on pelvic ultrasound * if serum hCG level \< 2 000 IU/L on a first measurement and serum hCG increases \<100% on a second measurement performed 3 days later * Highly effective contraception if the risk of conception exists. (Note: The effects of the trial drug on the developing human fetus are unknown; thus, women of childbearing potential must agree to use 2 highly effective contraceptions, defined as methods with a failure rate of less than 1 % per year. Highly effective contraception is required at least 28 days prior, throughout and for at least 60 days after avelumab treatment. * Patients who gave their written informed consent to participate in the study * Patients affiliated to a social insurance regime * Patient is 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. Cohort A specific inclusion criteria : \- Patients with gestational trophoblastic disease resistant to mono-chemotherapy (methotrexate and/or actinomycine-D Cohort B specific inclusion criteria : * Patients with gestational trophoblastic disease resistant to polychemotherapy (such as EMA-CO; EMA-EP; BEP; … regimens) without limitation in the number of previous chemotherapy lines * Patients with limited risk of fast progression, according to "Centre de reference des maladies trophoblastiques". In the case where a validated therapeutic alternative is available (platinum salt-based chemotherapy in case of resistance to polychemotherapy without platinum salt), the patient must have been informed and the therapeutic alternative will be proposed in priority. Exclusion Criteria: * Prior therapy with an anti-PD-1, anti-PD-L1, anti-PD-L2, anti-CD137, or anti- CTLA 4 (including ipilimumab, tremelimumab or any other antibody or drug specifically targeting T-cell co-stimulation or immune checkpoint pathways). * Illness, incompatible with avelumab, such as congestive heart failure; respiratory distress; liver failure; allergy. * 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, except those meeting the following criteria: * Brain metastases that have been treated locally and are clinically stable for at least 2 weeks prior to enrollment * No on-going neurological symptoms that are related to the brain localization of the disease (sequelae that are a consequence of the treatment of the brain metastases are acceptable) * Subjects with brain metastases must be either off steroids except a stable or decreasing dose of \<10mg daily prednisone (or equivalent) * Patients receiving any systemic chemotherapy, radiotherapy (except for palliative reasons), within 2 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 1) with the exception of alopecia and sensory neuropathy ≤ grade 2, 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. * Clinically significant (i.e active) cardiovascular disease : cerebral vascular accident/stroke (\< 6 months prior to enrollment), myocardial infarction (\< 6 months prior to enrollment), unstable angina, congestive heart failure (≥ New York Heart Association Classification Class II), or serious cardiac arrhythmia requiring medication * Patients with severe acute or chronic medical conditions including immune pneumonitis, inflammatory bowel disease, pulmonary fibrosis or psychiatric conditions including recent (within the past year) or active suicidal ideation or behavior; or laboratory abnormalities that may increase the risk associated with study participation or study treatment administration or may interfere with the interpretation of study results and, in the judgment of the investigator, would make the patient inappropriate for entry into this study. * Known severe hypersensitivity reactions to monoclonal antibodies, any history of anaphylaxis, or uncontrolled asthma (ie, 3 or more features of partially controlled asthma Global Initiative for Asthma 2011). * Known human immunodeficiency virus (HIV) or acquired immunodeficiency syndrome (AIDS) related illness. * Active infection requiring systemic therapy. * Positive test for HBV surface antigen and / or confirmatory HCV RNA (if anti-HCV antibody tested positive) * Administration of a live vaccine within 4 weeks prior the first dose of avelumab. * Treatment with oral anticoagulant such Coumadin. * Current or prior use of immunosuppressive medication within 7 days prior to start of study treatment. The following are exceptions to this exclusion criterion: * Intranasal, inhaled, topical steroids, or local steroid injections (eg, intra-articular injection); * Systemic corticosteroids at physiologic doses not to exceed 10 mg/day of prednisone or equivalent; * Steroids as premedication for hypersensitivity reactions (eg, CT scan premedication). * Active autoimmune disease that might deteriorate when receiving an immunostimulatory agents. Patients with diabetes type I, vitiligo, psoriasis, hypo- or hyperthyroid disease not requiring immunosuppressive treatment are eligible. * Female patients who are pregnant or lactating, or are of childbearing potential and not practicing a medically acceptable method of birth control * Resting ECG with QTc \> 470msec on 2 or more time points within a 24 hour period or family history of long QT syndrome. * Prior organ transplantation, including allogeneic stem cell transplantation (excluding autologous bone marrow transplant) * Known prior severe hypersensitivity to investigational product or any component in its formulations, including known severe hypersensitivity reactions to monoclonal antibodies (NCI CTCAE Grade ≥ 3) * Patients under guardianship.