I use the stand-alone forticlient package downloaded from the FortiNet support website, rather than the public repos. The client is in a zip package, and has no weird Ubuntu dependencies, so you just place it somewhere that makes sense, and run the script, eg:
Unfortunately you do require a valid https://support.fortinet.com/ login to download the files for Linux, but if you own FortiGate hardware, or know someone who does, then you can get it. Go to Download, Firmware Images (not very intuitive option!) and select product = FortiClient, and then click the download tab. The various OS options are listed.
To work properly the script requires root privileges... and it tries to detect 32-bit vs 64-bit architecture, before running the required sub-script.
Otherwise, as mentioned in the first answer, use the FortiNet repos directly.