There are lots of ways to answer this, so I'll go over some of your options.
Q: "If I put lowering springs on the car will I need to replace the shocks and struts?"
A: The short answer is no. No, you do not NEED to replace the shocks and struts in order to install lowering springs. HOWEVER, I would HIGHLY recommend doing so. If you ONLY add lowering springs, your car will be lower, but it will ride like a dump truck and you will wear out the stock dampers more quickly. More often than not, a specific lowering spring is developed to work with a specific set of dampers. If you install the springs in concert with the dampers you will get the lowered ride height you're looking for AND you will retain the ride quality (probably).
This ride quality also depends on how low you want to go. I went with Ford Racing for my suspension and I installed the 1" springs with the adjustable dampers, and when set to the softer end of the spectrum, the ride quality is even better than stock. However, if I had gone with the 1.5" springs on the same dampers, it would greatly deteriorate the ride quality. So you need to do some thinking and decide exactly what you want. Is having a low stance more important to you than ride quality? If so, perhaps the 1.5s are the way to go. If you want to actually enjoy driving your car, I'd go with the 1.0" ones.
Some people will combine a spring from one manufacturer with a damper from another and depending on the quality of the roads where you live, you may be fine with that, but in Michigan where I live, we have very bad roads, and I wanted as complete a setup as I could get.
Also keep in mind that many aftermarket dampers will also require an aftermarket strut mount in order to correctly fit the front struts to your car. You can go without them, but you will run into unwanted noise and vibration (which you definitely don't want). You will also want to think about upgraded jounce bumpers as well to keep the body from bottoming out so harshly on the axle when heavily loaded. And as previous posters mentioned, you will want to think about an adjustable panhard bar, too, as your axle is likely to shift a bit to the left or right after you lower the car.
I'd also highly suggest some upgraded rear lower control arms. There are lots of adjustable ones out there, but I went with the Ford Racing ones (which are actually GT500 units) and just making this mod, alone, makes a HUGE difference in how well the car can put its power down.
I hope that helps. Really the answer comes down to what are you looking to do and how much are you looking to spend. If all you care about is lowering the car as inexpensively as possible, you could just put on lowering springs and call it a day. If you want the car to actually handle better and last longer, you should do a comprehensive setup as I outline above.
If you have some money to spend, I'd recommend the Ford Racing Adjustable Handling Pack in the link below. It includes everything you need and is a really impressive setup. The adjustable shocks and struts feature 8 turns of adjustability - all the way left is soft (and is very comparable to stock), all the way right is firm and is excellent for track days and autocross sessions. The sway bars are adjustable three ways, depending on how much roll stiffness you want (or don't), and the panhard bar is fully adjustable to allow you to center the rear axle after the car has been lowered.
I've included photos of my car, before and after and also how my axle looked after being lowered, before the adjustable panhard bar.