Indeed the birth came after his accidental death. His widow never remarried to my knowledge. I will reinvestigate this though.
As for the Beaubien-Lamothe marriage I will also look for.
Jean de la Motte came from the parish of St-Michel in Bordeaux France. He kept to himself and did not leave much info about himself as he was a private man. We do know the name of his parents as he give them in 1698 when he got married to Marie-Anne Bruneau. She was a widow. The Notre-Dame church records are available on microfilm and can be borrowed at the JC Latter Day saints centres. Look for the entries of marriage and birth of most of his children.
Jean was the son of Matthieu and Jeanne Roselle. I am moving to France and will try to find more locally during the coming year.