He was the fifth son and youngest child of Francis I, Holy Roman Emperor, and his wife, Empress Maria Theresa.
In 1780, he succeeded his uncle Prince Charles Alexander of Lorraine as Hochmeister (Grand Master) of the Deutscher Orden (Teutonic Knights).
But when he arrived at the French Court he did not go by the name of Archduke Maximilian Franz, rather the pseudonym, the Comte de Burgau.
Thus he played an important role in the son's early career as a member of the same musical body of which his grandfather, also named Ludwig van Beethoven, had been Kapellmeister.
Recognising his young pupil's gift both as a performer and as a composer, Neefe brought Beethoven to the court, advising Maximilian Francis to appoint him as assistant organist.
Although Maximilian Francis still retained his territories on the right bank of the Rhine, including Münster and the Duchy of Westphalia, the elector, grossly corpulent and plagued by ill health, took up residence in Vienna after the loss of his capital and remained there until his death at the age of 44, at Hetzendorf Palace in 1801.