First guess, its a warped rotor. But if its shaking badly, you ought to be able to see such warping. (Have you pulled both the front tires and actually inspected the rotors on both sides?)
But after that: Shot steering linkage and stabilizer linkages in the front, or the control arm bushings. If you live in a winter cold climate zone, and its a 2004, the bushings and linkages are almost certainly shot. I'd guess control arm bushings first, probably the lower arm on one side or both.
My 1999 (in sunny near perfect Climate, no road salt, California) has nearly shot bushings, everywhere. Upper and lower control arm bushings (the rubber things at the arm pivots), the rubber boots on all the ball joints in the steering linkages are shot (but the ball joints are still OK for now), the stabilizer bar bushings are all cracked, and the stablizer linkages had actually failed (those I replaced). It ALL needs to be replaced, but I have been waiting for better weather to go do it.
If you live in a snowy or very wet winter zone, and especially if they use road salt where you live, then a 2004 model would be all done in the same way by now. Mine is only hanging in there because of mild climate.
When the lower (especially) or upper (a bit less) control arm bushings go, then on breaking, things will shake pretty badly.
You can inspect to some extent the control arm bushings, but the critical part is on the inside of the donut hole where the bolts go through the rubber cylinder, and you cannot really inspect that. But you can infer what kind of bad shape its in, if the outside of the rubber cylinders are cracked. If the outside is cracked, then the inside is shot (stretched out, compressed, cracking, and loose), and the lower and possible upper control arm bushing are done.
Though it is a very Big Bill, I would take it to a private mechanic that services Ford's, or specializes in suspension work, and work out a deal to get it all done at one time, because there is a huge labor savings. e.g. Get the upper, lower bushings, ball joints (whole upper control arm if he wants to go that way), Idler Arm, Steering (Pitman) Arm, inside and outside steering linkages, AND the stablizer bar bushings, and the stabilizer bar link connectors, ALL replaced at one time. I'd also have the proper alignment hardware installed (if missing, some Ford model years do not supply the cams), and you will need an alignment when that is all over (get that done at an alignment shop if the mechanic doesn't have an alignment setup). If you have it done all at once, you ought to be able to negotiate a 30% savings on the labor. So wait for the quote, and then ask for 30% off the labor quote. [He is saving perhaps 70% of the labor by doing it all together, but you won't ever get that. But 30% is reasonable.]
Unless you are going to do it all yourself. If so, and you are going to go "weekend of work at a time", then I would buy a new upper control arm with installed ball joint, And if you don't have a press, then a whole new lower control arm also, with bushings installed (rockauto) and the lower ball joint, and do that first on both the left and right front.
But a 2004, that has never had any of the front suspension elements changed, in a harsh winter climate, is due up I'm afraid. The rubber parts (bushings and boots) are all failing. When the bushings go on the control arms, you tend to get shaking, particularly when the lower control arm bushings go.
