Pulmonary Vein Isolation Alone or in Combination With Substrate Modulation After Electric Cardioversion Failure

Inclusion criteria: Criteria to be validated for patients included before performing electric cardioversion: 1\) Persistent AF (continuous for at least 7 days without interruption according to information transmitted by the cardiologist and the patient), symptomatic and resistant to at leat one anti-arrhythmic drug treatment including amiodarone; Criteria to be validated for patients included after performing electric cardioversion : 1. Patient treated by electric cardioversion for persistent AF, symptomatic and resistant to anti-arrhythmic treatment including amiodarone and whom ablative procedure is planned in the following 4-6 weeks after electric cardioversion Criteria to be validated for all patients included: 2. Life expectancy \> 5 years; 3. Female or male between 18 and 80 years of age at the electric cardioversion time 4. Affiliation to a health insurance system; 5. Patient informed of the study and having signed informed consent Criteria to be validated prior to randomization on the day of ablation (these patients may be randomized): 6. Patient with failed electric cardioversion i.e. in AF, confirmed by ECG. Exclusion criteria: Criteria to be validated before or after performing electric cardioversion (the study cannot be proposed to patients corresponding to these criteria): 1. Current hyperthyroidism; 2. Pregnant or breastfeeding woman; 3. Patient with a Body Mass Index (BMI) greater than 35; 4. Patient with severe Chronic Obstructive Pulmonary Disease (COPD); 5. Patient with hypertrophic heart disease; 6. Patient with a mechanical or biological mitral valve; 7. Contraindications to anticoagulants; 8. Transient Ischemic Attack (TIA) /stroke less than 6 months old; 9. Psychiatric illness affecting follow-up; 10. Left Ventricular Ejection Fraction (LVEF) \< 40% ; 11. Uncontrolled ischaemic heart disease (angina, myocardial ischaemia) 12. Patients under legal protection 13. Cardiac surgery on left atrium 14. Inflammatory status in progress (cancer, rheumatoid arthritis, PPRZ, acute or chronic periodontitis, Crohn's disease, RCUH) 15. Pulmonary embolism or phlebitis less than 6 months old 16. Prior atrial fibrillation ablation 17. Active cancer Criteria to be validated before randomization, on the day of ablation (these patients cannot be randomized): 18. Patient in sinus rhythm 4-6 weeks after electric cardioversion: these patients are included in the study registry. 19. Patient with complete absence of sinus rhythm (less than 10 seconds) after 3 electric cardioversion attempts: these patients will discontinue from the study.