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][1], also known as "_l’ordre mixte_" or simply the "_[manual of 1791]_"

[Petit manuel du canonnier, ou instruction générale sur le service de toutes les bouches à feu en usage dans l'artillerie][2] (1812)

In addition, I found this [Bibliography of French Military Manuals and Instructions Concerning the Napoleonic Period][3], which appears quite exhaustive, although you would need to visit the listed archives to consult the documents.

<hr>

**Great Britain** / **United Kingdom** :

[Rules and Regulations for the Formations, Field-exercise, and Movements, of His Majesty's Forces][4] (1792)

[Rules and regulations for the formations, Field-exercise, and Movements, of His Majesty's Forces][5] (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][6]  - John Russell (1804)

<hr>

**Austria**:

[Dienst-reglement für die Kaiserliche Königliche Infanierie][7] (1807)

and 

[Dienst-reglement für die Kaiserliche Königliche Cavallrie][8] (1807)


[Das Oesterreichische Militaer Betreffende Schriften][9] (1796)

<hr>

**Prussia**:

[Vorlesungen über die Taktik der Reuterey, von Einem Obersten der Reuterey][10] - Friedrich Wilhelm Graf von Bismark (1818)

[Handbuch für Officiere, in den anwendbaren Theilen der KriegesWissenschaften Von der Artillerie][11] - Gerhard von Scharnhorst (1787)

<hr>

**Spain**

(These manuals don't appear to be available on Archive.org, but can be found on Google Books)

[Tratado de Artilleria Vol 1][12] - Don Tomas de Morla (1816)

[Tratado de Artilleria Vol 2][13] - Don Tomas de Morla (1816)

[Tratado de Artilleria Vol 3][14] - Don Tomas de Morla (1816)

[Tratado de Tactica para la Infanteria Ligera][15] (1814)

[Tarifas de Todos los Haberes de un Regimiento Infanteria de Linea][16] (1802)

<hr>

**United States**:

[A hand book for infantry: containing the first principles of military discipline][17] - William Duane (1814)


  [1]: https://archive.org/stream/bub_gb_oVAf_0KIv-gC#page/n1/mode/2up
  [2]: https://archive.org/stream/bub_gb_Z3p4p0C9z_EC#page/n0/mode/2up
  [3]: http://www.napoleon-series.org/military/organization/c_regs.html
  [4]: https://archive.org/stream/rulesandregulat00commgoog#page/n10/mode/2up
  [5]: https://archive.org/stream/cihm_38147#page/n5/mode/2up
  [6]: https://archive.org/stream/instructionsfor00russgoog#page/n12/mode/2up
  [7]: https://archive.org/stream/bub_gb_XOOgAAAAMAAJ#page/n3/mode/2up
  [8]: https://archive.org/stream/bub_gb_kt2gAAAAMAAJ#page/n3/mode/2up
  [9]: https://archive.org/stream/dasoesterreichi02unkngoog#page/n9/mode/2up
  [10]: https://archive.org/stream/vorlesungenberd00bismgoog#page/n3/mode/2up
  [11]: https://archive.org/stream/bub_gb_PaQ6AAAAcAAJ#page/n3/mode/2up
  [12]: https://books.google.co.uk/books?id=eqovDCGysaIC&printsec=frontcover#v=onepage&q&f=false
  [13]: https://books.google.co.uk/books?id=I5zYgbLgWJIC&printsec=frontcover#v=onepage&q&f=false
  [14]: https://books.google.co.uk/books?id=YTXfy3cg9jEC&printsec=frontcover#v=onepage&q&f=false
  [15]: https://books.google.co.uk/books?id=JpRDYIyUnZEC&printsec=frontcover#v=onepage&q&f=false
  [16]: https://books.google.co.uk/books?id=oq7Ptvxx1NoC&printsec=frontcover#v=onepage&q&f=false
  [17]: https://archive.org/stream/handbookforinfan00duanrich#page/n7/mode/2up