See also thread:
http://forums.garmin.com/showthread.php?372146-Basecamp-cannot-see-or-import-fit-files-since-firmware-update-6-2
Since the change of the protocol of the .fit file (03-09-2017), Basecamp (version 4.6.2) cannot see or import .fit files anymore.
You can see the files in the file explorer of Windows (or Linux) but in the Windows program Basecamp 4.6.2 these files are invisible.
In Linux i use Qmapshack and there is the same problem.
luckily upload to Strava works.
As a workaround you can export .gpx files from Strava and import them into Basecamp (or Qmapshack)