When opening your Fusion model in the Autodesk 360 cloud interface, you can convert it to various formats, download the new version, then upload to Sketchfab.
From the Fusion 360 project side bar, click Open Details on Web.
On the Autodesk 360 page, open the Export dropdown and choose a supported format such as FBX, OBJ, or IGES. FBX is currently the best solution as it will preserve material settings.
It may take some time to finish the conversion. When the new version is ready, you can download it from the project page in Autodesk 360.
Local STL file
Fusion 360 can export STL files compatible with Sketchfab.
CAD software does not export textures because they don't use UV coordinates.
Open your model and go to File → 3D Print.
Disable the Send to 3D Print Utility option.
Click OK and Save the STL.
You can upload the STL to Sketchfab immediately or compress it into a ZIP/RAR/7z archive.