It looks to me as if Filemaker Pro on the MAC does have an ODBC interface. You can find out more about it here.

At that point your Filemaker Pro has become an ODBC datasource. Perl won't care very much that it is Filemaker Pro and should treat it like any other ODBC source.

I am not sure what the best way is to access ODBC from Perl. However, CPAN has some modules. DBD::ODBC available here looks like a promising candidate, but there may be better ways.