<p>From day 1 of my programming career, I started with object-oriented programming. However, I'm interested in learning other paradigms (something which I've said here on SO a number of times is a good thing, but I haven't had the time to do). I think I'm not only ready, but have the time, so I'll be starting functional programming with F#.</p>

<p>However, I'm not sure how to structure much less design applications. I'm used to the one-class-per-file and class-noun/function-verb ideas in OO programming. How do you design and structure functional applications?</p>

Given that modern functional languages (i.e. not lisps) by default use early-bound polymorphic functions (efficiently), and that object-orientation is just a particular way of arranging to have polymorphic functions, it's not really very different, if you know how to design properly encapsulated classes.
Lisps use late-binding to achieve a similar effect. To be honest, there's not much difference, except that you don't explictly declare the structure of types.
If you've programmed extensively with C++ template functions, then you probably have an idea already.
In any case, the answer is small "classes" and instead of modifying internal state, you have to return a new version with different state.