As I don't have a Fuji camera that shoots raw I can't tell you from first hand experience. What I can point you to is ufraw's information.
http://ufraw.sourceforge.net/Cameras.html Fuji E550
Fuji E900
Fuji F700
Fuji F710
Fuji F800
Fuji F810
Fuji S2Pro
Fuji S3Pro
Fuji S5Pro
Fuji S20Pro
Fuji S100FS
Fuji S5000
Fuji S5100/S5500
Fuji S5200/S5600
Fuji S6000fd
Fuji S7000
Fuji S9000/S9500
Fuji S9100/S9600
Fuji S200EXR
Fuji HS10/HS11
Fuji HS20EXR
Fuji HS30EXR
Fuji F550EXR
Fuji F600EXR
Fuji F770EXR
Fuji F800EXR
Fuji X-Pro1
Fuji X-E1
Fuji XF1
Fuji X-S1
Fuji X100
Fuji X10
Fuji IS-1
Since GIMP uses ufraw that's why I point you to there.
As for Darktable.
I point you to
http://www.darktable.org/usermanual/ch02s03.html.php2.3.1.3. Supported file formats
darktable is focused on managing and developing camera RAW files. It supports a huge number of file formats from various camera manufacturers. In addition darktable can read specific low dynamic range and high dynamic range images - mainly for data exchange between darktable and other software.
In order for darktable to consider a file for import, it must have one of the following extensions (case independent): 3FR, ARW, BAY, BMQ, CAP, CINE, CR2, CRW, CS1, DC2, DCR, DNG, ERF, FFF, EXR, IA, IIQ, JPEG, JPG, K25, KC2, KDC, MDC, MEF, MOS, MRW, NEF, NRW, ORF, PEF, PFM, PNG, PXN, QTK, RAW, RAW, RDC, RW1, RW2, SR2, SRF, SRW, STI, TIF, TIFF, X3F.
If darktable was compiled with JPEG2000 support, these extensions are also recognized: J2C, J2K, JP2, JPC.
If darktable was compiled with GraphicsMagick support, the following extensions are recognized in addition to the standard ones: BMP, DCM, GIF, JNG, JPC, JP2, MIFF, MNG, PBM, PGM, PNM, PPM.
Camera RAW files
darktable reads RAW files using two open source libraries: RawSpeed (developed by Klaus Post) and - failing that - with LibRaw. The number of supported cameras and file formats is constantly increasing. It is beyond the scope of this manual to give an exhaustive list. Most modern camera models are supported, and new ones tend to get added very quickly. darktable does not decode images from cameras with non-Bayer sensors (e.g. Fuji X-Pro1 or Sigmas with the Foveon X3 sensor).
LDR image files
darktable natively reads ordinary images in JPEG, 8-bit/16-bit PNG and 8-bit/16-bit TIFF format. JPEG2000 is also supported if the required libraries are built into darktable at compile time. Similarly, if darktable was compiled with GraphicsMagick support, there are further import formats, like GIF, Dicom DCM, additional exotic TIFF formats, and some of Sun's portable xyz-map family.
HDR image files
darktable reads high dynamic range images in OpenEXR, RGBE and PFM format.
If you don't want to download the programs and try it I would be willing to try it for you if you can provide me the file format in question. Since I have both GIMP and DT installed.
Chances are though, both should have no problem.
The grand thing about it is, downloading the programs is free so there's really no risk involved, such as spending money to find out it may or may not work, then trying to get a refund.