A Study to Evaluate the Effect of Venglustat Tablets on Left Ventricular Mass Index in Male and Female Adult Participants With Fabry Disease

This is an 18-month, multicenter, randomized, active-control, parallel-group Phase 3 study, in which participants will be randomized to venglustat versus standard of care therapy (agalsidase alfa, agalsidase beta, or migalastat) to evaluate the effect of venglustat on left ventricular mass index (LVMI) in adult participants with Fabry disease and left ventricular hypertrophy. * Study visits will take place approximately every 3 to 6 months * Participants who complete the randomized period may continue to the long-term extension (LTE) to receive venglustat for up to additional 45 months with the total study duration up to 5.3 years maximum.

Inclusion Criteria: * Male and female participants aged 18 to 65 with previously confirmed diagnosis of Fabry disease and a history of clinical symptoms of Fabry disease. * Participants may be receiving treatment with agalsidase alfa, agalsidase beta, or migalastat, or may be untreated. * Left ventricular hypertrophy. * Contraception for male or female participants: not pregnant or breastfeeding; no sperm donating for male participant. * A signed informed consent must be provided prior to any study-related procedures. Exclusion Criteria: * History of transient ischemic attack, stroke, myocardial infarction, heart failure, major cardiovascular surgery or kidney transplantation. * History of seizures currently requiring treatment. * Underlying medical condition that may cause or contribute to left ventricular hypertrophy. * Asymmetric hypertrophy by cardiac MRI at screening if considered by central reader to be not related to Fabry disease. * Advanced cardiac fibrosis, defined as significant late gadolinium enhancement affecting 3 or more segments involving \>50% of myocardial thickness on screening cardiac MRI. * History of clinically significant cardiac arrhythmia. Atrial fibrillation that is well controlled on a stable medical regimen for at least 12 months is not an exclusion if the CHA2DS2-VASc score is 0 for males or 1 for females. * Estimated glomerular filtration rate \