Inclusion Criteria:

          1. Histology :

               -  Soft-tissue sarcoma histologically confirmed. In care outside a center of the
                  RRePS Network, a central review is necessary (Pr. Coindre team),

               -  histologically confirmed ovarian carcinoma (carcinosarcoma included), or ovarian
                  carcinoma without known g/s BRCA mutation

          2. Ovarian carcinoma must have received at least one line of platinum-containing regimen

          3. Metastatic or unresectable locally advanced disease, not amenable to curative therapy

          4. Age ≥ 18 years,

          5. Eastern Cooperative Oncology Group (ECOG) performance status (PS) ≤ 1,

          6. Life expectancy > 3 months,

          7. Patients must have measurable disease (lesion in previously irradiated filed can be
             considered as measurable if progressive at inclusion according to RECIST 1.1) defined
             as per RECIST v1.1 with at least one lesion that can be measured in at least one
             dimension (longest diameter to be recorded) as > 10 mm with spiral CT scan.

          8. Documented disease progression according to RECIST v1.1 before study entry,

          9. Patient must comply with the collection of tumor biopsies,

         10. At least 1 line of chemotherapy in the palliative setting with use of Anthracyclines
             (for STS),

         11. At least three weeks since last chemotherapy, immunotherapy or any other
             pharmacological treatment and/or radiotherapy,

         12. Adequate hematological, renal, metabolic and hepatic function:

               1. Hemoglobin ≥ 9 g/dl (patients may have received prior red blood cell [RBC]
                  transfusion, if clinically indicated); absolute neutrophil count (ANC) ≥ 1.5 x
                  109/l, and platelet count ≥ 100 x 109/l.

               2. Alanine aminotransferase (ALT), aspartate aminotransferase (AST) ≤ 2.5 x upper
                  limit of normality (ULN) (≤ 5 in case of extensive liver involvement) and
                  alkaline phosphatase (AP) ≤ 2.5 x ULN.

               3. Total bilirubin ≤ ULN.

               4. Albumin ≥ 25 g/l.

               5. Calculated creatinine clearance (CrCl) > 60 ml/min (according to Cockroft Gault
                  formula).

               6. Thyroid function within normal laboratory ranges (TSH, free T3, free T4).

               7. Creatine Phosphokinase (CPK) ≤ 2.5 x ULN

         13. Women of childbearing potential must have a negative serum pregnancy test within 72
             hours prior to receiving the first dose of trial medication. Both women and men must
             agree to use a highly effective method of contraception throughout the treatment
             period and for six months after discontinuation of treatment.

         14. No prior or concurrent malignant disease diagnosed or treated in the last 2 years
             except for adequately treated in situ carcinoma of the cervix, basal or squamous skin
             cell carcinoma, or in situ transitional bladder cell carcinoma,

         15. Recovery to grade ≤ 1 from any adverse event (AE) derived from previous treatment
             (excluding alopecia of any grade and non-painful peripheral neuropathy grade ≤ 2)
             according to the National Cancer Institute Common Terminology Criteria for Adverse
             Events (NCI-CTCAE, version 4.0),

         16. Voluntarily signed and dated written informed consent prior to any study specific
             procedure,

         17. Patients with a social security in compliance with the French law .

        Exclusion Criteria:

          1. Previous treatment with Trabectedin or an anti-PD-1, anti-PD-L1, anti-PD-L2, including
             durvalumab

          2. Current or prior use of immunosuppressive medication medication including any use of
             oral glucocorticoids, within 21 days before the first dose of durvalumab, with the
             exceptions of intranasal and inhaled corticosteroids or systemic corticosteroids at
             physiological doses

          3. Active or prior documented inflammatory bowel disease (e.g., Crohn's disease,
             ulcerative colitis),

          4. Has an active autoimmune disease requiring systemic treatment within the past 2 years
             (ie, with use of disease modifying agents, corticosteroids or immunosuppressive
             drugs). Replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid
             replacement therapy for adrenal or pituitary insuddiciency) is not considered a form
             of systemic treatment,

          5. Has evidence of active non-infectious pneumonitis,

          6. Has an active infection requiring systemic therapy,

          7. Currently active bacterial or fungus infection (> grade 2 CTC [CTCAE] HIV1, HIV2,
             hepatitis A or hepatitis B or hepatitis C infections,

          8. Known central nervous system malignancy (CNS),

          9. Men or women of childbearing potential who are not using an effective method of
             contraception as previously described; women who are pregnant or breast feeding,

         10. Previous enrolment in the present study,

         11. Patient unable to follow and comply with the study procedures because of any
             geographical, social or psychological reasons,

         12. Has received a live vaccine within 30 days prior to the first dose of trial treatment.

             Note: the killed virus vaccines used for seasonal influenza vaccines for injection are
             allowed; however intranasal influenza vaccines (e.g., FluMist®) are live attenuated
             vaccines and are not allowed.

         13. Known hypersensitivity to any involved study drug or any of its formulation
             components,

         14. Tumors not accessible for biopsy,

         15. Known history of active tuberculosis

         16. Person under judicial protection or deprived of liberty,

         17. Cardiac dysfunction: LVEF < 40% at Baseline or clinically symptomatic cardiac
             dysfunction (any % of LVEF at Baseline)

         18. Concomitant use of strong inhibitor or inductors of cytochrome CYP3A4 taken within 21
             days prior to the first dose of study drug