We made grape jelly from the grape juice in the store when I was in high school. Gotta love Home Economics class. I still have the recipe, and it makes good jelly. We used the jar of ready to drink grape juice not frozen concentrate, but I think the concentrate works also, just remember to add the water to it.
However, it can be pretty hard to find real grape juice in the store now-a-days. Everything seems to be apple/pear juice flavored to taste like grape juice. You don't want "cocktail juice", you need to read the ingredients and make sure it is 100% grape juice.
I made some cherry juice a couple of months ago and am not really sure I like drinking cherry juice. I think I will try making cherry jelly with the rest of it.