I GIF file is an animated image, or a very compressed image. Your yellow smiley face you use as your sig image, is an animated GIF.
PSP4 should open them, they just don't work, or have their animated motion when opened in psp. Your pc should have come with PictureViewer as an orig. program. I use "Image Preview" to open up image files.
What I don't get is why PSP won't open one. Besides, you shouldn't have to open a GIF anyway, at least not in my experience. As long as mine will save things as a GIF, it's all I need. Other than that, I've only opened a gif in psp maybe once. So if it was me, I wouldn't worry about it.
If need be, you can always set a gif's properties to open with Internet Explorer, or a few other programs that come with your pc, that can used to open then, for viewing anyway. But if you want to modify a gif , then I can understand too. Then I'm all out of answers on this one.