I'm unsure where you have downloaded your FNS version so unless it's Pure Japanese Version that comes in a ISO, MDF, MDS file format I can't help you in general. You need to specify your media to make it easier for us to help you.
Personally I use Daemon Tools Lite to do the job. If it's one of the format I mentioned earlier, I would just mount it on as a DVD on Daemon Tools and then it should auto run so you can install from that point onwards. But I like the information on what media format you have so I can't give accurate information as to date.
For Example:
I currently have 3 Media Disks of Fate Night Stay. So what I do is:
Have Daemon Tools Lite Installed
Mount Disk 1 and have it go into autorun
Go into installation of the first disk
Complete my customized installation by ticking certain box and file path
Continue installing it and change the Disk when asked to do so
Then run the game to see if it will work
That's how I got my Fate Night Stay working on my computer in the past and it still works to be honest. So I have no idea why are you trying to extract it unless you have it compressed under something like zip or rar format.