Baricitinib in Patients With Relapsing or naïve Dermatomyositis

Inclusion Criteria: * Adult subjects (≥ 18 years old) \< 65 years old * Dermatomyositis defined according to the 239th ENMC criteria either naïve or non-naïve DM * Active disease (ACR/EULAR criteria) defined as : * Manual Muscle Testing (MMT-8) \<145/150 and at least two additional abnormal corset measurements (CSM): \>3/10 cm on Visual Analogue Scale (VAS) of patient global, physician global and extra-muscular disease activity, Health Assessment Questionnaire Disability Index \>0.25, or elevated muscle enzymes. * Or cutaneous CDASI \> 20 and at least two additional abnormal corset measurements (CSM): \>3/10 cm on Visual Analogue Scale (VAS) of patient global, physician global and extra-muscular disease activity, Health Assessment Questionnaire Disability Index \>0.25, or elevated muscle enzymes * for relapsing/non naïve DM patients : * in case of corticosteroid exposure patient must receive a stable dose \< 30 mg/d prednisone with or without additional immunosuppressive therapy for at least 4 weeks before the baseline visit. * Stable dose of immunosuppressive therapy for at least 3 months before * Affiliation to a social security regime * Written informed consent Exclusion Criteria: * Life-threatening complications : * Severe swallowing troubles defined as: food swallowed the wrong way and/or time to drink a glass of 200 ml water above 30 seconds related to DM. * Interstitial lung disease related to the DM with one among the following complications (complications must be related to the ILD): dyspnea NYHA III, hypoxemia with PaO2≤65 mmHg, and/or DLCOc/Alveolar Volume ≤70% (pulmonary function test) * Symptomatic myocarditis o Loss of walking ability * Patient with deep vein thrombosis/pulmonary embolism or antecedent * Patient with antecedent of cardiovascular event (myocardial infarction or ischemic stroke) * Patient who is current or past long-time smoker * Pregnant or lactating, or women planning to become pregnant or initiating breastfeeding * No effective contraception during the study and one week after for women of childbearing age * Renal impairment defined as clearance \< 60 ml * Strong Organic Anion Transporter 3 (OAT3) inhibitors * Active cancer or history of malignancy * Active severe infection including active hepatitis * Evidence of latent tuberculosis (as documented by a positive QuantiFERON-TB Gold plus test) * Absolute Neutrophil Count \< 1x109 cells/L * Haemoglobin (Hb) \< 8 g/dL * Severe hepatic impairment attested by FV (coagulation factor)\<30% * Liver insufficiency (Prothrombin time \<60%) * Previous treatment exposure defined as follow : • Rituximab treatment within 6months before inclusion * IVIg, or cyclophosphamide infusion within the month before inclusion * both methotrexate (0.3 mg/kg/w) and azathioprine exposure for at least 3 months each and at the 0.3 mg/kg/w and 2-3 mg/kg/d dosages respectively with failure of both (but exposure and/or failure to either of these two drugs alone is not an exclusion criterion) * for naïve DM patients only, more than 2 weeks treatment duration with corticosteroids at the dose of 1 mg/kg/d before the inclusion. * Hypersensitivity to the active substance (baricitinib) or to any of the excipients * Contraindication to Methotrexate and/or Azathioprine including hypersensitivity to the active substances or to any of the excipients * Conditions affecting the outcomes (Expected poor compliance) * Severe disease damages: e.g. muscle weakness mainly related to muscle damage such as fat replacement of muscle) defined as persistent changes in anatomy, physiology, pathology or function which result from previously active disease and from complications of therapy or other events (e.g.; muscle atrophy, fatty replacement; skin scars, poikiloderma ). Severe disease damage is considered when the patient condition has no or minor ability to improve with the treatment. * Significant uncontrolled cardiovascular, cerebrovascular, respiratory, hepatic, renal, gastrointestinal, endocrine, hematologic, or neuropsychiatric disorders, or abnormal laboratory values that developed during a qualifying study that, in the opinion of the investigator, poses an unacceptable risk for the patient's participation * Chest imaging (CT scan or radiograph) showing abnormalities not related with the DM in the last 12 weeks judged by the investigator as clinically significant. * Participants included in other intervention research involving humans * Patient under tutorship or guardianship, and incapable to give informed consent