You're right about it being a brook. Sorry, I was speaking generically.
How does one build walls overhanging the rive...er...brook?
You just do. You could build floors on the level of the surface of the water, walls to keep out the beasties, and more floors 1z up to cover it all up.
Passive Fist, your post isn't very helpful. Unless I'm mistaken, randyshipp here hasn't yet learned how to use
constructions, and thus doesn't know how to "just do".
To clarify the difference between brooks and rivers, randyshipp, brooks functionally have a 'floor' over them by default. This is to represent the fact that they're so shallow, and creatures could, theoretically, wade through them. Functionally, though, things can't get into the brook unless you purposely put a hole in this "natural covering", unless they're naturally residents of the waterway.
Judging by the layout of your map, you've actually got a great opportunity to create a fishing grotto.
First, on the level of the water, dig out an area roughly (picking a number at random) 5 tiles by 5 tiles, positioned so that there's only a one tile wall between the chamber and the water.
Secondly, on the level above that, dig out a chamber that is one tile wider on each side, without breaching the wall over the river (so, seven tiles wide by six tiles tall).
Third, once both chambers are excavated, follow the link I provided above and do a quick bit of reading up on constructions. As practice, try building a one tile wall in the access passage at the north end of the bottom chamber. Keep an eye on the dwarf building it to make sure he builds it from the north, not the south, so that he doesn't trap himself in the chamber. If he does get trapped, simply designate the construction to be removed ([d]->[n]), then read the section on the construction page titled "Avoiding Entrapment" for suggestions on how to prevent your suicidal dwarves from attempting to entomb themselves.
The next step is to designate channels on the top floor so that you have open access to the water chamber below. Be careful when doing this; if you do it all at once, you may have dwarves who stand on tiles others are trying to dig out, resulting in a short fall and a trip to the hospital once you tear down the wall to let them out of the bottom chamber. I find it easiest to designate one column of channels at a time, working from left to right.
If this works out, you should be left with a six by seven chamber on the upper floor, with a five by five hole in its middle. The bottom floor won't have any ramps, so anything in the hole can't climb out on its own; this is why I suggested digging the bottom chamber first. The option of digging out the upper room, then channeling the floor to create the bottom chamber is viable, and it does leave ramps around the edges.
Outside the fort, dig a short staircase down to the surface of the brook. This will serve two purposes - it'll let your dwarves walk on the surface of the brook for the purpose of letting the water in, and it'll let anyone who accidentally dodges into the canyon climb back out again. Making this staircase outside of your fort means that whatever winds up in there has to move away, rather than towards, in order to achieve this escape.
Now, on the upper level, in the middle of the south wall, designate one tile for channeling. If your dwarves can access the surface of the brook via the staircase mentioned above, one should trot off to climb down, then dig out the channel, which forms a two-story hole in the wall. Water will rush in from below and flood only the bottom chamber - but you're still left with a hole in the wall on the upper level.
Finally, designate a wall to be built in the hole on the upper level. Once again, a dwarf should trot down the staircase and along the surface of the brook to build this wall, and in so doing, seal off your little chamber from the outside world. Congratulations! You have now created a small fishing chamber inside your fort.
Hopefully this helps. If there's any part of my explanation that you'd like clarification on, or think would be easier to understand with a diagram, please let me know.