As I mentioned in the comments, there are many such manuals. The following have been digitised and made available as downloadable PDF files from Archive.org:
France:
Réglement concernant l'exercice et les manœuvres de l'infanterie, also known as "l’ordre mixte" or simply the "[manual of 1791]"
In addition, I found this Bibliography of French Military Manuals and Instructions Concerning the Napoleonic Period, which appears quite exhaustive, although you would need to visit the listed archives to consult the documents.
Great Britain / United Kingdom :
Rules and Regulations for the Formations, Field-exercise, and Movements, of His Majesty's Forces (1792)
Rules and regulations for the formations, Field-exercise, and Movements, of His Majesty's Forces (1811)
(It can be instructive to see how this manual changed over the period to incorporate lessons learned and developments in weapons and tactics.)
Instructions for the Drill, and the Methods of Performing the Eighteen Manoeuvres - John Russell (1804)
Austria:
Dienst-reglement für die Kaiserliche Königliche Infanierie (1807)
and
Dienst-reglement für die Kaiserliche Königliche Cavallrie (1807)
Das Oesterreichische Militaer Betreffende Schriften (1796)
Prussia:
Vorlesungen über die Taktik der Reuterey, von Einem Obersten der Reuterey - Friedrich Wilhelm Graf von Bismark (1818)
Handbuch für Officiere, in den anwendbaren Theilen der KriegesWissenschaften Von der Artillerie - Gerhard von Scharnhorst (1787)
Spain
(These manuals don't appear to be available on Archive.org, but can be found on Google Books)
Tratado de Artilleria Vol 1 - Don Tomas de Morla (1816)
Tratado de Artilleria Vol 2 - Don Tomas de Morla (1816)
Tratado de Artilleria Vol 3 - Don Tomas de Morla (1816)
Tratado de Tactica para la Infanteria Ligera (1814)
Tarifas de Todos los Haberes de un Regimiento Infanteria de Linea (1802)
United States:
A hand book for infantry: containing the first principles of military discipline - William Duane (1814)
In addition, Professor Kenneth Johnson (currently Deputy Department Chair of the Department of Research at the United States Air University’s Air Command and Staff College) wrote a paper in 2011 titled A Soldier Is Not a Soldier Without Training (PDF download), in which he discusses the training given to Napoleon's armies over time. He describes several of the texts that were used in his paper, which might be of interest to you.