You are incorrect.
Napoleon was recruited for the coup because it couldn't be done successfully without a general because the army was the only stable institution in France. The Directory was both ineffective and corrupt. Sieyes recognized this and he was one of the Directors. His intention was to use a general officer to effect the coup and then with his other conspirators form a new government that was hopefully better than the Directory and rule France.
The general was merely the 'sword.'
Sieyes didn't bargain on Napoleon being much more talented and competent than they believed.
So, it wasn't a military coup, any more than Napoleon's rule was a military dictatorship. Napoleon ruled as a civilian head of state and never as a military dictator. The overwhelming majority of the ministers and functionaries of Napoleon's government were civilians, not soldiers. There were a few exceptions such as Carnot, Berthier as Minister of War from 1800-1807, and Savary who became Minister of Police in 1810-but that was not the rule.