Currants are tiny berries that are frequently used to make jams and jellies. Although foods containing added sugar, such as fruit spreads, are not necessarily Paleo, currants, by themselves, are.
Paleo and Fruit
Although people sometimes differ when determining whether to include fruit in their Paleo lifestyle, berries are frequently a source of common ground. These little fruits are usually high in antioxidants and low in sugar, hence the tendency to add sugar when making them into fruit spreads. On their own, though, currants can make an excellent addition to a Paleo lifestyle.
Mark Sisson condones eating berries for their high antioxidant capacity on his blog.