One option would be to use ODBC to access the FileMaker tables from Microsoft Access - I haven't used Access myself but I assume it can perform ODBC queries?
If so you could setup the FileMaker Pro database as the source (if you're hosting the FileMaker file with FileMaker Server you will need to use FileMaker Server Advanced) and query the database via ODBC. Have a look at the FileMaker ODBC Guide for more details:
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You can make ODBC connections in Access with FM Tables. Here is a link with some helpful information.
Note: In Windows, Microsoft Access can import only 32 or fewer fields at one time via ODBC from a FileMaker database file. If your database file has more than 32 fields, import them in increments of 32.
One note that is easy to miss...to use FileMaker as a datasource you can either use FileMaker Pro/Advanced on the same machine as your front-end program, or you need FileMaker Server Advanced if you are working over a network.