Bureau was born in Champagne and moved to Paris where he worked for the English government during the occupation.
In 1439 Charles VII made Bureau master of artillery in his army. He then served in the sieges of Pontoise and Harfleur in Normandy and the capture of Bayeux. In 1453 he led the French army at the Battle of Castillon that defeated Sir John Talbot, 1st Earl of Shrewsbury in what is considered the last battle of the Hundred Years War. In his work as master of artillery for the king of France Jean Bureau was assisted by his brother Gaspard Bureau (1393-1469).
Later he was made Lord of Montglat, Mayor of Bordeaux and knighted in 1461.
Jean Bureau died in Paris on July 5, 1463.