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