What is your definition of 'a legitimate government?' Napoleon didn't lead the coup in 1799. He was recruited for it by the leaders. Unfortunately for them, Napoleon proved to be a master of the new situation rather than merely a sword. If Napoleon had not taken part, the leaders of the coup would have found another soldier to do the dirty work.

It would be interesting to find out how the Hohenzollerns, Romanoffs, and Hapsburgs came to be 'legitimate' rulers. The Bourbon, Henry IV, had to fight for his crown and was later assassinated for his trouble.

Napoleon generally gained the approval and acceptance of the French people. He crowned himself in order to demonstrate to the French people that he was not beholding to the Church as Emperor of the French or anyone else for that matter. Monarchs just didn't show up. They generally, at one point, had to fight to become monarchs, one way or another. Alexander either had his father murdered and/or at least approved of the murder. I wouldn't say that his way to the throne was 'legitimate.' He became Tsar through murder of his own father.

Sincerely,
Kevin