That is the entire issue. Using FileMaker data files is in no way expected (that I'm aware of) in a browser. What you learned with Access is pretty much it other then ODBC based connection. For ODBC connection, an ODBC driver (interpret's the file) must exist. No one has made one that I'm aware of for FileMaker. I'm certain one can be written using C/C++ and having the FileMaker's data structure in hand. I wouldn't be shocked if FileMaker's format is nothing more then DBX (dBase derived).
The point is, it would be easier to convert the data to Access outside of the server, use it in that format. If someone want's it back, convert it back.
Doing connection processes (ADO) is pretty much the same with all data formats using an ODBC connection, but if the ODBC driver does not exist, the connections isn't going to happen without an unrealistic amount of work to do so.
I could write a custom data format faster then I could figure out what FileMakers is if that gives you any insite.
Good luck.
Brian