In addition to the Weinachtsmarkt (Christmas market) in downtown Kaiserslautern, the Fructhalle, a concert hall also downtown, is hosting a market. Its German name is Kulturmarkt vor Weihnachten in der Fruchthalle.
It's basically an arts and crafts market. I stopped by last weekend and perused the fine art (i.e painting and sculpture) as well as ceramics, knitted items, jewelry, Christmas decorations, etc. Everything was quite nice and handmade. I picked up a ceramic soap dish for eight euros.
In addition to the arts and crafts, there is food for sale. I didn't sample anything, but saw freshly made waffles, desserts, and soups for sale.
The Fructhalle is located right across from the tourists' information office downtown. The market is open from 25 November until 22 December and is open daily from 12 p.m. - 7 p.m. On 12-13 December it is open until 8 p.m. There is no admission charge.