Can't you just use filesystem permissions? Like, FoxPro under its own user and it's database owned and accessible by FoxPro user only?
The rub here is that FoxPro is an in-process database engine and accesses its data files with the security context of the user running the application. It doesn't have separation between the database engine and the UI like a client/server database would. Think of it like SQLite or BerkeleyDB.
Architecturally users who use the application need full read/write access to all the data files for FoxPro to work.