You may be a little puzzled by a shot towards the very end when Captain Renault dumps out a bottle of Vichy water and tosses it in the trash. The motivations are hinted at in the movie but—because most people knew all about it at the time the movie was made—it doesn't go into a lot of detail. So here's the skinny.
When the Germans defeated France, they divided the country into two. They themselves occupied the eastern half of the country—including Paris, the actual capital— but because they had bigger fish to fry (including a very big scary one called Communist Russia), they set up a puppet government in the western half of the country, with a capital in Vichy France. Technically, Vichy was neutral in the war, but they basically danced to the Germans' tune…and because they controlled Casablanca and other French colonies, we can see that playing out in the film.
In direct terms, Renault's dumping his Vichy water signals that he's no longer willing to be the puppet. He's ready to fight the Germans just like Rick is. But on a subtler level, it also makes a very pointed statement about the U.S. government's position on the whole thing. Roosevelt was much more interested in stopping Germany than stopping Vichy, while the Nazis would happily throw Vichy at the Allies in order to save themselves. So Vichy become this sort of elephant in the room that no one talked about, and everyone played along with them being "neutral" to keep their eyes on the Germans, instead of having to actually fight the Vichy French.
Casablanca clearly has some things to say about that. Germans? Vichy French? They're all the bad guys! And the film states quite strongly that we need to treat them as such instead of pretending that they don't exist.