Pilot Study to Assess Efficacy and Safety of Sofosbuvir/Ledipasvir Fixed-dose Combination in Treatment Experienced Subjects With Hepatitis C Virus (HCV) Genotype 1 - HIV Co-infection

Inclusion Criteria: * Confirmed HIV infection * Infection with HCV genotype 1 only, confirmed at screen visit, with a HCV-RNA ≥ 1000 InternationalUnit(IU)/mL at screen visit * Treatment-experienced subjects with: * previous virological failure to tritherapy with Peginterferon/Ribavirin and protease inhibitor, * or premature discontinuation of previous tritherapy with Peginterferon/Ribavirin and protease inhibitor due to intolerance to Peginterferon or protease inhibitor * Anti-HCV treatment stopped for at least the last 3 months * Patients on a stable (for more than 1 month) antiretroviral treatment consisting of an emtricitabine/tenofovir or lamivudine/tenofovir standard of care backbone plus efavirenz or raltegravir or rilpivirine or enfuvirtide. Alternative combinations of the above listed medications may be allowed. * Dendritic cells 4 \> 100/mm3 and \> 15% at screen visit * HIV-RNA \< 50cp/ml for more than 3 months at screen visit * Any liver fibrosis grade, with the assessment of the presence or not of cirrhosis at screening, cirrhosis being defined as a METAVIR score of F4 on the liver puncture biopsy and/or with hepatic impulse elastometry ≥ 14,5 kilopascal (kPa): * Previous liver biopsy exhibiting cirrhosis lesions (METAVIR F4), * and/or significant liver biopsy (cumulative length ≥ 15mm or ≥ 5 portal spaces), within the past 18 months * and/or significant and reliable liver stiffness assessment (Fibroscan®) within the past 6 months (at least 10 measures with IQR less than 30% of the median value and a success rate of at least 70%). * Female patients with child-bearing potential, and their heterosexual partners must use adequate contraception from the date of screening until 90 days after administration of the last dose of study drug. Male participants must agree to consistently and correctly use a condom, while their female partner must use adequate contraception from the date of screening until 90 days after administration of the last dose of study drug * Body weight ≥40 kg and ≤125 kg * Informed and signed consent for the main study and the Pharmacokinetic (PK ) sub-study (for the participating patients) * Patients with Health insurance Non inclusion Criteria: * Child-Pugh B or C cirrhosis or history of decompensated cirrhosis. * Co-infection with Hepatitis B virus (HBV) (AgHBs +) with HBV DNA \> 1000 UI/ml * Pregnant or breast-feeding women * Transplant recipients * Opportunistic infections (stage C), active or occurred within 6 months prior to baseline * Evolutive malignancy, including hepatocarcinoma which should be controlled prior to baseline * Alcohol or drug consumption which may affect the study participation according to the investigator. Patients included in a programme of substitution with methadone or buprenorphine could be enrolled. The opinion of a consultant in addictology is recommended for patients presenting with current drug use or drug use during the previous year. * Patients with a history of non-adherence, who will be at risk of being unable to respect the study follow-up timetable * Patients participating in another clinical trial within 30 days prior to inclusion * Hb \< 10 g/dL (female) or \< 11g/dL (male) * Platelets \< 50 000/mm3 * Neutrophil count \< 750/mm3 * Renal failure defined as creatinin clearance (MDRD) \< 60ml/min * Other antiretroviral drugs than those allowed in the study * Contra-indications to Sofosbuvir, Ledipasvir * Contra-indicated treatment likely to interfere with the study drugs as listed in the protocol