The Batavian Republic is located in Holland. It is initially allied to France, and is at war with the Coalition. Despite being allied to France and at war with the Coalition, it has historical grievances with France and strong historical friendships with half of the factions in the Coalition, as well as Prussia (who usually fights France sooner or later). It begins the game in a trade agreement with France. It borders Belgium, Cleves-Mark, and Oldenburg, held by France, Prussia, and Oldenburg, respectively.
Due to its strong historical greivances with France, it is an unreliable ally at best, and tends to break alliances with France rather than join in its defence. If it can be convinced to make peace with coalition members, it enjoys very strong relationships with them. It usually allies with neighboring Oldenburg fairly early on in the campaign.
Despite its small size, the Batavian Republic can field multiple, large armies if left to its own devices. While its unit roster is limited, preventing its armies from being too powerful, the quantity of the units it can produce can make it a powerful regional threat. The region of the Netherlands itself is quite rich, with a large city, a port, and a school. This makes the Batavian Republic a good candidate for invasion.
The Batavian Republic is permanently removed from the game if defeated; it cannot emerge. If the Netherlands rebels or is liberated, the United Netherlands emerges instead.
The Batavian Republic is unique in that it is the only faction in Napoleon: Total War that is available for sea battles in multiplayer, but not land battles (where they are replaced by the United Netherlands). They have an unremarkable, small ship roster. One particular weakness of theirs is their lack of Ironclads.