I believe you need to use the VisualFoxpro.FoxApplication
class, and you are passing invalid syntax - to execute a VFP program you need to use the DO
command:
var parse = new VisualFoxpro.FoxApplication;
string foxCommand = "do init.prg";
parse.DefaultFilePath = @"\\TestFox\FoxPrograms";
parse.DoCmd(foxCommand);