The date I have found for the war of the Second Coalition is November 1798. You might well be correct about the involvement of Turkey/Ottoman Empire being a result of the French invasion.
However, the object of the expedition to interdict the British trade route to India is legitimate. And if you are 'aware' of the Directory being the approving authority for the expedition, then putting almost the entire responsibility for the expedition being authorized on Napoleon is wrong.
If you have Herold's book, then look at pages 6-15 regarding the background of French intentions regarding the Ottoman's and Egypt. Talleyrand was the main instigator or the expedition, not Napoleon, for example.