Short answers, pulled from the story.
Auxonne served for centuries as a border town between the Duchy of Burgundy and the County of Burgundy, making it a strategic military stronghold on the boundary between French and Holy Roman Empire territory. It also housed the Artillery School where Napoleon Bonaparte was stationed from 1788 to 1791.
Napoleon Bonaparte was stationed in Auxonne as a lieutenant from 1788 to 1791, auditing classes at the Artillery School. His teacher there was the mathematician Jean-Louis Lombard, who lived from 1723 to 1794.
Henry III issued letters patent on the 1st of May 1586 declaring the people of Auxonne guilty of lèse-majesté because they repeatedly refused to accept Claude de Bauffremont, the king's appointed governor, and continued to demand the Baron of Pluvault instead. The dispute stemmed from the town's resistance to the Duke of Mayenne and the Catholic League during the French religious wars. An accord signed on the 15th of August 1586 at Tillenay revoked the charges and exempted Auxonne from taxation for nine years.
Auxonne was transferred to the Duchy of Burgundy on the 15th of June 1237, through an exchange agreement concluded at Saint-Jean-de-Losne between John Count of Chalon and Hugh IV Duke of Burgundy. In return, Burgundy gave up the Barony of Salins and ten strategic positions.
The engineer Vauban took over the fortification works at Auxonne after the Count of Apremont died in 1678. He completed the Royal Gate in 1699 and built the Arsenal between 1689 and 1693, originally used for manufacturing gun carriages. Vauban had planned a larger project but lost interest after the Treaty of Nijmegen was signed in 1678, so the full scheme was never completed.
The Bonaparte Museum is housed in a tower of the Chateau d'Auxonne and displays objects from Napoleon Bonaparte's time stationed in the town, including his set square, his fencing foil, and items he left during his stays. The barracks where he lived, built in pink Moissey stone, now serve the 511th Logistics Regiment.