Study Comparing Efficacy of Doxorubicin With Trabectedin Followed by Trabectedin Versus Doxorubicine in Patients With Leiomyosarcoma

Inclusion Criteria: 1. Patients must have histologically confirmed diagnosis of metastatic or relapsed unresectable uterine or soft tissue leiomyosarcoma, reviewed in a reference center (among RREPS network), previously untreated with chemotherapy , and with available Formalin Fixed Paraffin Embedded (FFPE) blocks 2. At least one measurable lesion according to RECIST V 1.1 criteria. Target could be in a previously irradiated field but has to be progressive or a biopsy had to be positive before inclusion. 3. Age ≥ 18 years old 4. ECOG performance status \< 2 (Appendix 4) 5. Adequate haematological, liver and cardiac functions: * Neutrophil counts ≥ 1500/mm3 * Platelets ≥ 100 000/mm3 * Serum creatinin \< 1.5 x Upper Limit of Normal Value (UNL) * Serum bilirubin ≤1 x ULN * ALT, AST ≤ 2.5 x ULN * Alcaline phosphatases ≤ 1.5 x ULN * Cardiac ultrasound and/or normal isotopic ventriculography : Shortening Fraction (SF) \> 30%, Left Ventricular Ejection Fraction (LVEF) \> 50% 6. Creatinin phosphokinase (CPK) ≤ 2.5 x ULN 7. Women of childbearing potential (WOCBP) must have a negative pregnancy test within 7 days prior to inclusion. Both males and WOCBP who are sexually active should be using an effective birth control method from inclusion (for WOCBP) or treatment initiation (for male) and up to 6 months following the last dose of study drug. 8. Signed written informed consent form 9. Patient affiliated to a social security regimen or beneficiary of the same Exclusion Criteria: 1. All other histological types of uterine sarcomas or soft tissue sarcomas 2. Any contraindication for the use of trabectedin and/or doxorubicin (cardiac, renal, hepatic, known hypersensitivity…) 3. Patient already enrolled in another therapeutic trial involving an investigational substance, and when such a substance has been taken during the previous 4 weeks. 4. Medical history of progressive psychiatric disorder 5. History of another type of cancer not in complete remission for more than 3 years prior to study entry (except for cutaneous basal cell carcinoma or in situ cervical epithelioma), and/or having required any chemotherapy treatment at any time. 6. Known cerebral metastasis 7. History of allograft or autograft 8. Active viral hepatitis B or C or known human immunodeficiency virus (HIV) infection or any other uncontrolled infection 9. Pregnant women or nursing mothers 10. Patient under guardianship or deprived of his liberty by a judicial or administrative decision or any condition (e.g., psychological instability, geographical location, social reason, etc.) that, in the judgment of the Investigator, may affect the patient's ability to understand and sign the informed consent or to fully comply with all study visits, treatments, procedures, and other requirements scheduled in the protocol.