Yes Fred Meyer Jewelers will replace watch batteries whether in watches that they sold to you or watches that you bring into them even though you purchased the watch somewhere else.
I've taken a watch into Fred Meyer Jewelers and they actually replaced the battery for no charge and didn't even charge me for the battery.
They said they did that to hopefully get you as a customer to buy other things and some people do eventually come back to them or decide to buy something from them.
However I'm not sure if the Fred Meyer Jewelers still replaces watch batteries for free but it's been awhile.
However Fred Meyer Jewelers will still likely replace the watch battery even at a small charge or for the price of the battery.