When connecting to a Parquet file, the FDM UI doesn't display the tables or columns available for masking.
FDM 4.10.268.0 or greater
The filename of the parquet file, is 90 characters in length. The Windows operating system limits the File Path + File Name (combined) to not exceed 256 characters.
Renaming the parquet file to use a shorter name resolved the issue.
Note: another option would be to use a shorter file path.