There are probably several ways to do it, but I would use the string search feature of std::string class
std::string line = "<FILE_NAME>Testfile.dat</FILE_NAME>";
std::string filename;
size_t pos;
if( (pos = line.find("<FILE_NAME>") > string::npos)
{
filename = line.substr(pos+11);
// truncate the </FILE_NAME> tag
pos = filename.find('<');
filename = filename.substr(0, pos);
}