You can install FortiClient (macOS) 6.2.4 on macOS 10.15 Catalina, which Apple released in early October 2019. With this macOS release, however, FortiClient works properly only when you grant permissions to access the full disk in the Security & Privacy pane for the following services:
The FortiClient (macOS) Web Filter feature works properly only when you allow system software from Fortinet to load in Security & Privacy settings. Go to System Preferences > Security & Privacy and click the Allow button beside System software from developer "Fortinet, Inc" was blocked from loading. You must have administrator credentials for the macOS machine to configure this change.