Effect of Weekly GLP1 Agonist Treatment in "Double Diabetes"

Inclusion Criteria: * Person who has given written consent * Patient over 18 years of age * Patient with type 1 diabetes confirmed by a C-peptide below laboratory standards * Age at diagnosis \< 35 years * Treated with optimized insulin therapy (multi-injections or pump) for at least 1 year, having received specific therapeutic education on insulin dose adaptation. * BMI (weight/height2) ≥ 27 Kg/m². * At least one of the following criteria: * Family history of type 2 diabetes (parents, grandparents, uncles, aunts, brothers and sisters) * Family history of obesity (BMI\>30 Kg/m2) (parents, grandparents, uncles, aunts, siblings) * Triglycerides \> 1.50g/l (1.7mmol/l) * HDL\< 0.5 g/l (1.29 mmol/l) in women, HDL\<0.4 g/l (1.03 mmol/l) in men * HbA1c ≥ 7.5% and \< 12% in the 3 months preceding inclusion * Having continuous glucose monitoring by a CGM (Holter Glucose Monitoring) system: Guardian, Dexcom or Free Style Libre * For women of childbearing age: using an effective method of contraception until 2 months after the end of treatment. Effective contraception includes: hormonal contraception, intrauterine device, bilateral tubal occlusion, vasectomy and sexual abstinence Exclusion Criteria: * person not affiliated to national health insurance * Pregnant, parturient or breastfeeding woman * HbA1c ≥12% in the 3 months preceding inclusion. * Uncontrolled and potentially unstable diabetic retinopathy or maculopathy, confirmed by a fundus examination performed in the 6 months preceding the selection * Person under a measure of legal protection (curatorship, guardianship) * Renal insufficiency (GFR\<30 ml/mn) * Hepatic insufficiency (INR\> 1.5) * BMI \>40 kg/m². * History of bariatric surgery * History of pancreatitis * Allergy to the active substance or to one of the excipients of OZEMPIC®. * Patients who have received GLP-1 agonist therapy or who received such therapy within the year prior to enrollment * Patients who have received oral antidiabetic therapy within the month prior to enrollment