Why did Napolean fight through Europe all the way to Crimea? What was his goal?
It seems unlikely that this was purely due to empire expansion as I don't see how this would be feasible over such a short time.
Well you have to look at the various different wars Napoleon fought, his goals were not always the same.
That being said, there are some themes that one can look at to analyze why Napoleon fought and why he demanded certain things in peace treaties.
The biggest one is security, Napoleon was not loved by the old monarchies of Europe, especially in Russia, Austria, and Britain where the French Revolution and Napoleon were seen as dangerous to the traditional European order. A lot of the wars Napoleon fought were actually not by his own choosing, many of the coalition wars were declared against Napoleon. And to a large part his peace treaties reflect this; intending to give France client states and buffers against the other powers of Europe. Now this isn't to say Napoleon didn't have his own imperial ambitions, the invasion of Spain being a key example of a war of aggression. But even in that example Napoleon was largely motivated by a desire to prop up an important French ally (his mistake was replacing the Spanish dynasty with a Bonaparte one). France did annex some areas, but generally Napoleon wanted to build up his allies by giving territory from defeated enemies to make his allies strong and better able to aid France.
Another one was recognition, not only of Napoleon's dynasty, but of his allies. A lot of Napoleon's peace treaties stipulated that his enemies must recognize the countries created by Napoleon, and while this wasn't as big a factor as security, Napoleon certainly felt it important to legitimize the new order he created, and warfare was a way to do that.
But as I mentioned above, those goals aren't always present. For example, one can look at the invasion of Russia (what I assume OP was referring to), which was intended to force Russia to adhere to the continental system. The continental system was Napoleon's attempt to starve out Britain, who were almost always working against Napoleon either through building new coalitions or encouraging new countries to take up arms against "the Corsican ogre". The system tried to starve put Britain by banning all continental trade with Britain. The Continental system was a failure, and Russia felt that abiding by it would hurt their economy, Napoleon was still rather hopeful that it would work and so set out to try and execute a quick campaign to destroy Russia's army and force them back into the system.
Please look here for an answer I gave to another.