Narcolepsy is a sleep disorder that disrupts a person's regular sleep-wake cycle. It causes extreme sleepiness during the day (called excessive daytime sleepiness [EDS]), where a person may fall asleep without warning. Narcolepsy Type 1 (NT1) is a form of the condition in which people also have sudden, unexpected muscle weakness while staying conscious (called cataplexy).

The main aim of this study is to learn how safe TAK-360 is and how well adults with NT1 tolerate it. Adults who can participate in the study will have to stop taking their existing medicines for NT1 before study treatment starts. Participants may be randomly (by chance, like drawing names from a hat) assigned to get either TAK-360 or placebo during the treatment period. The placebo looks just like TAK-360 but does not have any medicine in it. After the treatment period, participants can be monitored for another 2 weeks. Participants can restart their usual NT1 treatment after study treatment ends.

The participants will have to visit the clinic multiple times during this study.

Key Inclusion Criteria:

1. The participant has a body mass index within the range 18 to 40 kilograms per meter square (kg/m^2) (inclusive).
2. The participant has an International Classification of Sleep Disorders, Third Edition (ICSD-3) or ICSD-3 Text Revision diagnosis of NT1.

Key Exclusion Criteria:

1. The participant has a current medical disorder, other than narcolepsy with cataplexy, associated with excessive daytime sleepiness.
2. The participant: (a) has a history of myocardial infarction; (b) has a history of clinically significant thyroid disease, coronary artery disease, cardiac rhythm abnormality or heart failure.
3. The participant has a clinically significant history of head injury or head trauma.
4. The participant has a history of epilepsy, seizure, or convulsion (except for a single febrile seizure in childhood).
5. The participant has a history of cerebral ischemia, transient ischemic attack (<5 years from screening), intracranial aneurysm, or arteriovenous malformation.
6. The participant has a history of cancer in the past 5 years (does not apply to participants with carcinoma in situ that has been resolved without further treatment or basal cell carcinoma; these participants may be included after approval by the medical monitor).
7. The participant has a positive test result for hepatitis B surface antigen, hepatitis B core antibody, hepatitis C virus antibody, or human immunodeficiency virus (HIV) antibody/antigen at screening.
8. The participant plans to participate in any other interventional trial while participating in TAK-360-2004 or has previously participated in another part in TAK-360-2004.
9. The participant has a known hypersensitivity to any component of the formulation of TAK-360 or related compounds.

Takeda provides access to the de-identified individual participant data (IPD) for eligible studies to aid qualified researchers in addressing legitimate scientific objectives (Takeda's data sharing commitment is available on https://clinicaltrials.takeda.com/takedas-commitment?commitment=5). These IPDs will be provided in a secure research environment following approval of a data sharing request, and under the terms of a data sharing agreement.

IPD from eligible studies will be shared with qualified researchers according to the criteria and process described on https://vivli.org/ourmember/takeda/. For approved requests, the researchers will be provided access to anonymized data (to respect patient privacy in line with applicable laws and regulations) and with information necessary to address the research objectives under the terms of a data sharing agreement.