The
while
statement should be at the beginning of the block, before you get the film details, and a do loop would probably work better:
do
{
cout << "Enter the film name name: " << endl;
getline(cin, filmname);
if (filmname == "end")
break;
cout << "Enter the director's name: " << endl;
getline(cin, director);
full = filmname + " " + director;
cout << "The film and director is therefore: " << full << endl;
Film.push_back(full);
} while (true);