The thing about the titles and accolades is that they change over time: like I said before, Imperator was originally a term for a big-time general or commander, and then after the founding of the Roman Empire, they started using it as a sovereign head of state. 200 years later, they introduced the title of Caesar to mean basically the same thing, which is where the Holy Roman Empire gets the title Kaiser from once power goes to the Germans. And even then, the Kaiser was elected for life by the Bishops of the realm (feel free to fact check me on that; it's been awhile since I took German History).

We also see the title of King change over time. Traditionally, the king was 'elected' not unlike how you would decide where your friends want to go to dinner: whoever gets the loudest approval and least complaining grunts gets their way. We see this with Armenius of the Cherusci, who commanded the Germanic tribes in the destruction of Rome in 9 AD, but was later deposed and killed once he tried to rule over the people in a top-down, Romanesque manner. Fast forward to Medieval Europe and you see this king-authority granted by the "divine right of kings" instead of by plurality. Fast forward to today, and you still have kingship based off of lineage, but with very little socio-political power.

So to answer your question, you're probably not wrong; but also remember that they had just deposed King Louis XVI of Bourbon in 1792. I'm honestly not too familiar with France and the French Empire under the House of Bonaparte, but I imagine Napoleon was trying to restore the Carolingian Empire under French rule or something like that. Boys and their toys, y'know?