Well, if it makes the noise when the car isn't moving, that eliminates quite a lot. A screeching noise is usually a belt or a bearing, and with the wheels stationary, that knocks it down to the remaining moving components, the engine and transmission. Like I said, a belt is the first thing anybody would look for, and they're pretty easy to diagnose. Remove that and I'd put my money on the transmission/torque converter. Since it stops screaching when you put it into reverse, I'd lean towards the tranny, as the torque converter would be constant as long as the engine's running. I've never owned a FWD car, so I'm far from an expert, but I believe that the tranny/tc is pretty close to the front pax wheel. The good news is that it probably shouldn't be too bad a fix on that car.
Another reason I'm leaning that direction is that after replacing the spark plugs in my car about 3 months ago, it made a horrific screaching noise, which turned out to be a bearing in the torque converter. 3 months and 1500 miles later I'm still driving it. In my case, the labor cost exceeds the value of the car, so I'm just gonna drive it until it stops moving. If I were you, I'd take it to a competent mechanic, let him listen to it with a stethescope and pinpoint the noise. If it is the tranny, have him replace the fluid and the filter. I probably won't solve the problem, but it might and it's a helluva lot cheaper than replacing either part. The rationale is that good ATF should expand to fill volume when it gets hot. If it's bad (or completely empty), that's not happening and it can cause some real problems with the car.
Standard disclaimer: I'm not a mechanic, and I've never owned a FF car. Drivetrains are complicated business, and there are a lot of things that could make a noise. I'm just speculating.