I don't eat fries with burgers. A burger on it's own is a fine meal, you don't need the fries. And if you really like fries, why eat them with burgers when there are so many things they go much better with ? If you're one of the people who eats either first, why did you order both if you don't plan on eating them like a meal ?
At home, a little of both, at restaurants, sometimes the same, but sometimes the burger first and then the rest of the fries. Never all of the fries first, that's just kind of... Weird. If I were on my way home from a restaurant, I guess I would have some fries first though. I don't go to restaurants that much though; maybe once or twice a month.
Usually, burger first. My mother always impressed upon me, as a child, to eat the more "expensive" or "important" item first. French fries are filler, the burger is the more important item. So I could leave fries without feeling bad. My dad would usually sweep in and take care of those.