Notice that I have passed the FileStream to the ProcessFiles. This creates a readlock on the file, making it impossible to let the file being opened by another program or thread. You use the FileStream to read the acquired file (eg StreamReader sr = new StreamReader(myFileStream) ).

VerifyCopyComplete.cs

string[] existingFiles = Directory.GetFiles(ProcessPath, "*.xml");
foreach (string fileName in existingFiles)
{
            FileInfo fi = new FileInfo(fileName);
            FileStream fs = null;
            while (fs == null && fi.Exists)
            {
                try
                {
                    fs = fi.Open(FileMode.Open, FileAccess.Read, FileShare.None);
                }
                catch (SecurityException se)
                {
                    break;
                }
                catch
                {
                    Thread.Sleep(100);
                }
            }
            if (fs != null) ProcessFiles(fs);                             
}