Check the surface of the pearls and look for cracks (especially around the drill holes) and discoloration in general on the surface. If the pearls were not well-cared for they may have a distinct yellowish coloration to them.
A strand this old would not be a piece that would be sold in your typical jewelry store unless they specifically deal with antique jewelry. You would need to find a buyer that is interested in the era. I would suggest something like a jewelry auction, but it would definitely behoove you to appraise them first. I suggest Northwest Gem Labs in Boise Idaho. Sharon Wakefield should be able to give you an accurate assessment and valuation. This would be the best way to authenticate them as South Sea pearls. It is very likely that a jeweler would not be able to do a good assessment. In my experience most jewelers cannot tell the difference between a round, high-quality freshwater pearl and an Akoya or South Sea. One that could give you an accurate valuation would be extremely difficult to find.
Please find her contact info below:
Sharon Wakefield
sharon@gem-science.com
208-362-3938