As listed in the Wikipedia link on the War of the Fifth Coalition:
Austria lost ~20% of its population through ceded territory and had to pay heavy fines while not yet totally defeated in 6 months of warfare, which is by no means leniency.
A complete breakup of Austria by military means would have likely required further resources from an already strained French economy after decades of postrevolutionary struggles and an ongoing continental blockade.
Ongoing war or too harsh a punishment for Austria would have also opened up the possibility of intervention by the other Great Powers, all of which favored a reverse to a balance of power in Europe and the restoration of the pre-revolutionary Monarchy in France.
Likewise, a complete humiliation,defeat and breakup of Austria would have only further stoked nascent German nationalism, which, contrary to its revolutionary rhetoric, was not in the interest of France given its recent acquisitions of German territories. The Holy Roman Empire, for the longest time under Austrian leadership was only dissolved 3 years before the end of the war.
Losses of Austria in the Treaty of Schönbrunn: https://www.britannica.com/event/Treaty-of-Schonbrunn
General overview of the war: http://www.historyofwar.org/articles/wars_franco_austria_1809.html based on the books 1809: Thunder on the Danube: Napoleon's defeat of the Habsburgs, Vol 1-3, John H. Gill
Sources on nascent German Nationalism (examples):
Tyrolean nationalist rebellion during the war: https://en.wikipedia.org/wiki/Tyrolean_Rebellion
Assassination-attempt on Napoleon based on German nationalism at the signing of the peace treaty of the war: https://en.wikipedia.org/wiki/Treaty_of_Sch%C3%B6nbrunn#Assassination_attempt
Dörnberg-uprising in Hessen during the war: https://en.wikipedia.org/wiki/Wilhelm_von_D%C3%B6rnberg#D%C3%B6rnberg's_Uprising_(22%E2%80%9324_April_1809)
German Source: Archduke Charles, stating that Austria took up arms not only for Austrian independence, but for German independence and German national honor («Nicht bloß für seine Selbständigkeit, sondern für Deutschlands Unabhängigkeit und Nationalehre» habe Österreich das Schwert ergriffen.): Napoleon I. by August Fournier, p. 289 https://books.google.de/books?id=fWV9yHRNjW0C&pg=RA1-PA289&lpg=RA1-PA289