Not really. (string[0] == string[0].toUpperCase() && string[0] != string[0].toLowerCase()) is the correct way to approach this problem. If toUpperCase() and toLowerCase() don't handle Turkish letters, then that's a BUG in those methods, which should be reported and someone should freaking take responsibility for them and fix them.
Adding another module with a method does not fix the original problem, it just creates more problems for other people to solve.
Adding another module with a method does not fix the original problem, it just creates more problems for other people to solve.