"The one thing you can't do with bayonets is sit on them!"--Napoleon Bonaparte
Aside from the question of whether the British would allow Napoleon to enjoy his conquests in peace, I suppose he'd always be thinking in terms of another battle, another zone where he isn't satisfied with the situation and sends in his armies that can't sit on their weapons but must be used somewhere; he's bound to get in over his head somewhere some time, and then the system of hegemony he's set up would tend to come unglued, with the British (assuming they've gone unconquered or without domestic revolution in his favor) constantly worrying at the weak seams and many of the peoples, or anyway ruling dynasties, he has subjugated jumping at the chance to throw him off, it wouldn't take much to signal his imminent downfall.
He can't disband his armies, nor can they sit in occupation for decades. Well, these declarations might be the thing for an enterprising TL author to contradict; a Napoleonic Europe seems like it might be some fun to me--I definitely think Napoleon was a more admirable figure than Hitler anyway and there was much to be said by a lot of people--the Poles, the Jews, for instance--in favor of the French ideals he spread.
I do think he'd suffer from an inability to know when enough was enough; his enemies would continue to work to overthrow his system and the more he conquered the more weak seams there would be (arguably though he might, if astute enough, recruit more allies as well).
The problem of succession remains; to whom would he trust handing the system over to, and would that favored heir be competent to keep it together?
I don't think he had enough political vision to set up a reasonably foolproof system, unfortunately. He was wiser than a lot of would-be rulers, but not superhuman, and this wasn't his strongest point by any means. Once a big part of his reliable French forces got the stuffing kicked out of them (or more accurately, starved out) in Russia, he was on the ropes. Those men with bayonets were the foundation of his power and he'd lose too many of them somewhere or other, likely even if he had the wisdom to avoid unnecessary adventures and probably even if he did.