* `line_count` can be obtained with `len(lines)` instead of an enumerate.
* You use `rstrip` (rightstrip), I think that `strip` is better as you (probably) don't want to count the blanks of indentation as characters.
* `f` is the standard name for files in Python not `fin`
* Using list comprehension and a for loop as you do is much more readable than a functional alternative, anyway, down here I show you a functional version:

:

    def code_metric(file_name):
        with open(file_name) as f:
            lines = f.read().splitlines()
        char_count = sum(map(len,(map(str.strip(),filter(None,lines)))))
        return len(lines), char_count