This is a single group Phase 1/Phase 2, 1-arm, open-label study with SAR444836, an adeno-associated virus (AAV) vector-mediated gene transfer of human phenylalanine hydroxylase (PAH), for the treatment of adult participants with phenylketonuria (PKU) on a chronic, stable diet. The purpose of the study is to evaluate the safety and efficacy of SAR444836 in reducing phenylalanine (Phe) levels and in the elimination of a Phe restricted diet. Participants will receive a one-time intravenous (IV) administration of SAR444836. The study is constituted of 2 separate parts: a dose escalation part, and a dose expansion part where subsequent participants will be administered a safe and effective dose level identified during the dose escalation part. In both study parts, clinical and laboratory assessments will be collected to: a) assess the incidence of adverse events, and b) evaluate the effect of SAR444836 on reductions in blood Phe levels and maintenance of these Phe levels after elimination of a Phe restricted diet. The study duration will be approximately 102 weeks (approximately 2 years) for each participant and includes a 6-week screening phase and 96-week follow-up period after SAR444836 administration. There will be a total of 41 study visits. Many study visits may occur as remote visits and be performed by a qualified in-home service provider. Actual study duration for an individual participant may be longer than 102 weeks due to the administration of SAR444836 to participants in Stage 1A in a serial fashion, or other factors such as delays in scheduling study visits.