Capture One does not belong to Fuji.
There are free, basic versions (Capture One Express) for Fuji, Sony and Nikon:
Get Capture One's flagship photo editing software, trusted by pros and studios worldwide. Capture One Pro supports files from all major camera brands.
www.captureone.com
Get Capture One's flagship photo editing software, trusted by pros and studios worldwide. Capture One Pro supports files from all major camera brands.
www.captureone.com
These are the same download as other versions of Capture One, but you get a licence key that unlocks a non time-limited version with fewer features than the full product.
Fuji's own software is called Raw File Converter. Like Nikon's previous package, Capture NX (not sure about Studio), it's built on Silkypix:
This software is made by “Adwaa Co., Ltd.”. When you install it, you need to accept “Adwaa Co., Ltd. License Agreement”.
fujifilm-x.com
They also have a package that uses your camera's processor to do the raw conversion:
Download the latest version for FUJIFILM X RAW Studio.
fujifilm-x.com