FileInfoFullNameファイルへのフルパスを取得するために使用できるプロパティが含まれています
var fullNames = files.Select(file => file.FullName).ToArray();
小切手
私のマシン上のこのコード:    
FileInfo[] files = null;
string path = @"C:\temp";
DirectoryInfo folder = new DirectoryInfo(path);
files = folder.GetFiles("*.*", SearchOption.AllDirectories);
//you need string from FileInfo to denote full path
IEnumerable<string> fullNames = files.Select(file => file.FullName);
Console.WriteLine ( string.Join(Environment.NewLine, fullNames ) );
版画
C:\temp\1.dot 
C:\temp\1.jpg 
C:\temp\1.png 
C:\temp\1.txt 
C:\temp\2.png 
C:\temp\a.xml 
...
完全なソリューション
問題の解決策は次のようになります。
string path = @"C:\temp";
DirectoryInfo folder = new DirectoryInfo(path);
var directories = folder.GetDirectories("*.*", SearchOption.AllDirectories);
IEnumerable<string> directoriesWithDot = 
 directories.Where(dir => dir.Name.Contains("."))
            .Select(dir => dir.FullName);
IEnumerable<string> filesInDirectoriesWithoutDot = 
 directories.Where(dir => !dir.Name.Contains("."))
            .SelectMany(dir => dir.GetFiles("*.*", SearchOption.TopDirectoryOnly))
            .Select(file => file.FullName);
Console.WriteLine ( string.Join(Environment.NewLine, directoriesWithDot.Union(filesInDirectoriesWithoutDot) ) );