Hello! If you are related to the Wrens then you are related to me somehow. I found a second cousin right here in Dallas when I was doing genealogy. She is also related to the Wrens from there and she lived in Coushatta for a while. My great grandparents lived in Coushatta. If the family are Wrens and the town is Coushatta then it is definitely Red River Parish. I dont know what you may have found with a listing of Natchidoches but I am thinking there may have been some confusion on a cesus card or something. I do know that several of my own relatives lived in Coushatta but were in Natchidoches for a while due to enlisting in the Civil War.
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Oh also in Coushatta there is a cemetery called the Wren Cemetery. Actually I think it is in Martin which is a little community outside of Coushatta.