Early in their French studies, students learn that rêver means "to dream" and un rêve is a dream. So far so good. But the expression "to have a dream" (when you're asleep) in French is not "avoir un rêve" but faire un rêve. By the same token, "to have a nightmare" is faire un cauchemar.
However, avoir is used if you mean "harboring a dream": je n’avais aucun rêve secret d’Élysée means "I wasn't harboring any secret dreams of becoming the President of France."
Then there is the expression faire rêver, literally "to make dream," but that won't work as a translation into English. Here are some examples:
l'histoire d'amour qui a fait rêver l'Amérique
the love story that captured America's heart
Le monde occidental a atteint un bien-être matériel qui fait rêver le reste de la planète.
The industrialized world has achieved a material prosperity that the rest of the planet dreams of.
Un voyage à Paris au printemps fait rêver.
A trip to Paris in the springtime is the stuff dreams are made of.
Rêver can also turn up in contexts like the following:
--Oui, un rêve, je sais ...
Yes, it's wishful thinking, I know...
Encore des rêves...
It's just more wishful thinking.