Nassau (as a duchy) existed above the Rhine It was near the end where the river came near the French border.
Nassau was also south of the Prussian Empire, Not near the coast of the Rhine. It was named after it's centre Nassau, but it was not its capital. When it helped in Waterloo it ended up in Belgium near Planciontot before being absorbed into Prussia.
They engaged the French on many occasions, clearly capable of standing up to the French however they were ultimately deafened after an engagement at the town of Smohain and the farm of Frichermont, they became part of the Confederation of the Rhine, Ending their independence, they were annexed by Prussia and became an independent state. Later, Nassau helped in the Battle of Waterloo before being absorbed into the Prussian Empire, and later, the empire of Germany.