It depends who you ask and what place and time you're talking about, because title usage conventions tend to be quite fluid.
I think Napoleon I was copying the usages prevalent up to that time. The formal title of the Holy Roman Emperor was "Emperor of the Romans", so Napoleon crowned himself "Emperor of the French". The notion that he was a popular monarch was only loosely associated with the title; I think it came more as the only plausible way of justifying a royal or imperial dignity for himself, as a commoner who rose to prominence as a military leader in a republican movement, apart from naked force.
I think Napoleon III used the same title as his uncle in order to emphasize continuity, as his claim was based on bloodlines and inheritance.
At about the same time as N3, there was a nontrivial controversy in the negotiations about the formation of the German Empire over the Kaiser's specific title. The Kaiser-to-be wanted to be "Emperor of Germany" (which he saw as implying that the government and constitution drew their legitimacy from him, not the other way around), while the federated German monarchs generally preferred "German Emperor" for precisely the same reasons. In terms of actual constitutional role, though, the Kaiser and N3 were very similar: they were strong, hereditary executives of constitutional states and were considered to be of imperial dignity.
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