Inclusion Criteria:  Male or female; Age between 18 and 75 years-old; Adult patient with a diagnosis of RA as defined by the ACR/EULAR 2010 criteria for the classification of RA; Patient who presents an inadequate response to one to four bDMARDs or tsDMARDs for at least 12 weeks prior to study entry at a dose that is considered acceptable to assess clinical response adequately; Patient affected by active RA (DAS28-ESR > 3.2) eligible to receive a bDMARD or tsDMARD according to the French Society of Rheumatology guidelines; Patient treated by prednisone dosage ≤ 10mg per day. The corticosteroids dosage will be decreased to 7,5 mg/day at the beginning of the study (W0); Person affiliated with or beneficiary of the French social security scheme; Free, informed and written consent signed by the participant and the investigator (on the day of inclusion at the latest and before any examination required by the research project).  Exclusion Criteria:  Patient previously treated with baricitinib or adalimumab for RA; Patient affected by another form of inflammatory arthritis with the exception of secondary Sjögren syndrome; Patient who presents contraindications to the study treatments; Patient who is currently receiving glucocorticosteroids at doses >10 mg of prednisone per day (or equivalent) or has been receiving an unstable dosing regimen of corticosteroids within 4 weeks of study entry; Patient who is currently receiving more than 1 concomitant csDMARD (MTX, leflunomide, hydroxychloroquine or sulfasalazine) at the time of study entry; Patient who is currently receiving or has received csDMARDs (eg, gold salts, cyclosporine, azathioprine, or any other immunosuppressives) other than MTX (up to 25 mg/week), leflunomide (up to 20 mg/day), hydroxychloroquine (up to 400 mg/day), or sulfasalazine (up to 3000 mg/day) within 4 weeks prior to study entry. Doses of hydroxychloroquine or sulfasalazine should be stable for at least 4 weeks prior to study entry; if either has been recently discontinued, the patient must not have taken any dose within 4 weeks prior to study entry. Immunosuppression related to organ transplantation is not permitted; Patient who has received any parenteral corticosteroid administered by intramuscular or intravenous injection within 4 weeks prior to study entry, or is anticipated to require parenteral injection of corticosteroids during the study; Patient who had 3 or more joints injected with intraarticular corticosteroids or hyaluronic acid within 4 weeks prior to study entry. Joints injected with intraarticular corticosteroids or hyaluronic acid within 2 weeks prior to study entry or within 6 weeks prior to planned randomization cannot be counted in the TJC and SJC for entry or enrollment purposes; Patient with haemoglobin less than 80 g/L, absolute lymphocyte count lower than 0.5×109/L, absolute neutrophil count less than 1×109/L, or platelet count less than 100×109/L; clearance creatinine less than 60 mL/min; total bilirubin more than 1.5 times the upper limit of normal (ULN) at screening, aspartate aminotransferase, or alanine amino-transferase more than 2 times the upper limit of normal (ULN) at screening. Patient with co-administration with OAT3 inhibitors (such as probenecid); Patient who has a history or presence of cardiovascular, respiratory, hepatic, gastrointestinal, endocrine, hematological, neurological, or neuropsychiatric disorders or any other serious and/or unstable illness that, in the opinion of the investigator, could constitute a risk when taking investigational product or could interfere with the interpretation of data; Patient with an history of Moderate to severe heart failure (NYHA classes III/IV); Patient with an history of Major Adverse Cardiovascular Events (non-fatal myocardial infarction or non-fatal stroke); Patient who has a history of Venous Thromboembolic Event (VTE) (DVT/PE) within 12 weeks prior to randomization or have a history of recurrent (>1) VTE (DVT/PE). Prior DVT with PE where events overlapped in time (i.e., with PE considered resulting from DVT) is not considered recurrent DVT/PE for the purpose of this criterion. Patient who has been exposed to a live vaccine within 12 weeks prior to planned randomization or are expected to need/receive a live vaccine during the course of the study (with the exception of herpes zoster vaccination). Investigators should review the vaccination status of their patients and follow the local guidelines for adult vaccination with nonlive vaccines intended to prevent infectious disease prior to entering patients into the study; Patient with an active cancer; Patient with malignancy or history of malignancy in the past 5 years, with the exception of adequately treated or excised non-metastatic basal-cell or squamous-cell cancer of the skin or cervical carcinoma in situ; Patient who has a current or recent (<30 days prior to study entry) clinically serious viral, bacterial, fungal, or parasitic infection; Patient who is immunocompromised and, in the opinion of the investigator, is at an unacceptable risk for participating in the study; Patient with a history of active hepatitis B virus (HBV), hepatitis C virus (HCV), or human immunodeficiency virus (HIV); Patient who had household contact with a person with active tuberculosis (TB) and did not receive appropriate and documented prophylaxis for TB; Patient who has evidence of active TB or has previously had evidence of active TB and did not receive appropriate and documented treatment; Patient who has evidence of latent TB (as documented by a positive Purified Protein Derivative (PPD), no clinical symptoms consistent with active TB, and a normal chest x-ray at screening) unless patient completes at least 3 weeks of appropriate treatment prior to study entry and agrees to complete the remainder of treatment while in the trial Patient who had any major surgery within 8 weeks prior to study entry or will require major surgery during the study that, in the opinion of the investigator, would pose an unacceptable risk to the patient; Pregnant or breastfeeding woman, or woman who refuses to use an effective contraception during the study course; Patient governed by articles L 1121-5 to L 1121-8 (persons deprived of their liberty by a judicial or administrative decision, minors, persons of legal age who are the object of a legal protection measure or unable to express their consent).