Project Euler #22 - Names Scores
Your code is split into small functions and looks nice.

A few things could be done in a better way.

zip(count(1),sorted(names) can be rewritten with the enumerate builtin : enumerate(sorted(names), start=1).

You can iterate directly over strings so you don't need to use a list in list(name).

You don't need parenthesis in for (ind, name) in.

To answer your question :


FILE could easily be moved behind the main guard so I'd put it there. Had it been the smallest of the issues, I would have left it where it currently is.
for the with, I consider it to be a good habit to put it. Also, this should answer your solution.