Impact of Omega 3 in Alcohol Use Disorder

The goal of this clinical trial is to investigate the biological pathways underlying the beneficial effect of omega-3 polyunsaturated fatty acids (n-3 PUFA) on mental health in patients with alcohol use disorder. The main questions this study aims to answer are: * Can n-3 PUFA improve mood disorders (depression, anxiety), craving for alcohol, cognitive impairments and sociability disorders ? * Are the beneficial effects of n-3 PUFAs due to a modification of the gut microbiota and/or the inflammatory status? Participants will : * take a supplementation of omega-3 or placebo during 3 months * do a brain MRI * be interviewed for a dietary anamnesis * provide blood, stool and saliva samples * perform psychological tests and neuropsychological tasks Researchers will compare active comparator (omega-3) with placebo comparator (olive oil) to see if omega-3 can have a beneficial effect on AUD patients.