It depends on how "dBaseIII" oriented the table really is. Some of the earlier versions going way back have different file header information and that may be the issue. In that case, you might need to do a one-time process of opening and copying the VFP version table to a dBaseIII format, then move that into the production path for your connection.
if you use the Microsoft Visual Foxpro OleDb Provider, you can connect to the path where the table is, and execute a script something like
USE YourTable
COPY to NewVersion TYPE FOXPLUS
Disadvantage of older dBASE file formats is it does not recognize the corresponding index files without being explicitly opened and won't optimize queries... but again that is based on very old dBASE file formats.