The first thing is I don't really see the contrast itself as a problem. I see the lighting as more of an issue (which certainly affects contrast). Improved lighting (more on this later) would improve the scene by bringing out more highlights in the silver parts and more color in the jeweled parts. Your background is going into saturation, but this is not necessarily a bad thing. For jewelry photography, usually you want to minimize anything involving the background or anything else in the shot for that matter, and driving it into saturation is one way to do that. One problem you have is the detail found in the cloth in the areas that are in focus. You don't really want that. A smooth cloth or paper, or having those areas go out of focus is a good way to deal with that. I like to use white poster board as a background. It's perfectly smooth, you can bend it, and best of all it's extremely cheap. Cloth attracts all sorts of lint, dust, hairs, and all sorts of other things that can show up in the in-focus areas and ruin the shot.
As far as focus goes, I don't really like to include out of focus areas in the foreground. The eye is naturally drawn to the foreground, so adding out of focus subjects in the foreground is a source of distraction. That's not to say that this is a hard and fast rule, but more often than not it's better not to include out of focus areas in the foreground. That's just my tastes, but I'm not the only photographer that feels that way.
As others have suggested, you can photograph small subjects on a piece of plexiglass. However, while this can produce dramatic effects, it can also produce it's own set of problems. Lighting becomes much trickier, and the plexiglass has to be pristine for the in-focus areas. Any scratch, crack, or mark will show up.
One of the easiest ways to photograph jewelry (or any small objects for that matter) is to build yourself a lightbox. It's ridiculously simple and cheap to do and you can find all the materials at your local hobby shop. This one is similar to the one I built.
http://strobist.blogspot.com/2006/07/how-to-diy-10-macro-photo-studio.html
Instead of tracing paper, I found a transluscent poster board type material at my local hobby shop which I used for the sides and top. The example above shows a strobe used for the lighting. If you don't have a strobe you can use off camera (I don't think your camera has a hot shoe or PC connector than makes off camera strobe triggering practical), you can use a desk lamp or just about any other light source (or multiple light sources), you can come up with. If you use multiple light sources, make sure they are all the same type. In other words, if you use an incandescent light for one light source, don't use a flourescent for the other unless you're making a black and white shot. For whatever light source you use, adjust the white balance either on the camera or in photoshop until the white background is perfectly white.
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