Friedreich Ataxia is a rare condition that causes damage to the nervous system and muscles. People with Friedreich Ataxia have difficulty walking, lose sensation in their arms and legs, and have slurred speech. It can also affect the heart and many people with Friedrich Ataxia develop serious heart problems. Friedreich Ataxia is a genetic condition which means a faulty gene is passed down through families. This type of gene therapy treats a genetic condition by providing a healthy copy of the gene. At the time this study started, there was no approved treatment for heart problems in people with Friedreich Ataxia. In this study, ASP2016 is being tested in humans for the first time. The people taking part are adults with Friedreich Ataxia who have heart problems. The main aims of the study are to check the safety of ASP2016 and how people cope with (tolerate) ASP2016. ASP2016 is given as a slow injection into a vein. This is called an infusion. People will also take tablets of a medicine called prednisolone. This is taken to stop the immune system interfering with ASP2016. Each person in the study will be given 1 single infusion of ASP2016. Different small groups will receive lower or higher doses of ASP2016. Each person will stay overnight in the clinic for at least 1 night after their infusion. For the first few months, people will visit the clinic regularly. There may be the option of home visits by a study nurse at some visits. At the 6-month and 12-month visits extra tests, procedures, and scans will be done. One of these is an ECHO (echocardiogram) scan. This is like an ultrasound scan for the heart. Another is an endomyocardial biopsy. A tiny piece of their heart tissue is removed (biopsy). A flexible hollow tube (catheter) goes into the blood vessels up to the heart. Then, a small device on the end of the catheter takes a tiny piece of heart tissue (about the size of a pencil tip). Another is a cardiac MRI. This takes pictures of the inside of the heart using a powerful magnet. Another is a cardiopulmonary exercise test (CPET). This involves moving a specially designed set of bicycle pedals using hands and arms. This will check how the lungs, heart and muscles are affected during exercise. After the 12-month visit, people will visit the clinic every few months for up to a few years.