You can certainly find tools or converters that can be used for the purpose of fbx to gif conversion, but the results might wary depending on the solution.
If you want to have best control over the output, it would be best to use some 3d modeling tool with GIF export. You can also try out of one of the online converters (For example Aspose), then the result will most likely be a GIF that contains one view/slice of the 3d model.
Probably works best with small FBX files.