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François Baugis (1586/7 - ? after 1667) arrived in Beauport, Quebec in 1641. The name Baugis in Canada went through various spellings before settling on Bougie. Joseph Baugis (1752-1831) left Beauport at 14 and went to Kaskaskia, an island in the Mississippi River. In the U.S. the name also went through several variations before settling on Bogy.
François Baugis's family tree is here: https://www.geni.com/family-tree/index/6000000006583701156.
There are probably other Bougies who are not descended from or related to François Baugis; I don't know.
—Eric MacKnight, April 2022