Use T-SQL to return free space on a network share
I'm not sure if this will give you exactly what you want, but you could try this:

DECLARE @cmd VARCHAR(2000)
SET @cmd = 'DIR "\\SHARENAME"'

EXEC xp_cmdshell @cmd


The last line would give you the freespace

output
04/04/2016  05:39 AM            15,872 TrackSqlLogins_0_131042360126710000.xel
08/15/2014  07:01 AM               449 TransparentDataEncryptionCertificate
08/15/2014  07:01 AM               636 TransparentDataEncryptionCertificatePrivateKey
              13 File(s)  1,208,231,169 bytes
               8 Dir(s)  217,800,073,216 bytes free