Note: The genetic origin of the Vermette name is, in my mind, uncertain. Anthoine was born in a region that changed government several times over the 1500s and 1600s. The regions was hotly contested by France, Spain, Germany, and the Dutch. In addition, Arras is in the path to the narrowest part of the English Channel and was therefore overrun by armies going both ways across the channel, starting with the Romans in the fourth century. Whatever his genetic origins, Antoine was culturally French in that he was a member of the French Catholic church, lived in a border region that spoke French, and emigrated to the colony of new France about 1645 either as a soldier in the French Army or as a farmer.
From the Encyclopedia Britannica:
Of Gallo-Roman origin, it was the chief town (Nemetacum or Nemetocenna) of the Atrebates, one of the last Gallic peoples to surrender to Julius Caesar. The woollen industry dates from the 4th century. The Middle Ages was a period of great material and cultural wealth, when Arras became the English word for tapestry hangings. The fortunes of the town followed those of troubled Artois, and it passed through many hands before being joined for the last time to France in 1659 by the Treaty of the Pyrenees. A peace treaty (1435) was signed there by Philip III (the Good) of Burgundy and Charles VII of France. The Peace of Arras in 1482 fixed the northern frontiers of modern France. From 1479 to 1484 Louis XI, after razing the walls, ordered a mass deportation of citizens. Arras was the birthplace of Maximilien de Robespierre. The French Revolution and both World Wars destroyed many of its ancient buildings. The town centres on two arcaded and gabled squares, the Grande and Petite. The reconstructed 16th-century Gothic Hôtel de Ville is on the Petite Place.