I think the noun "locale" is not much used in spoken English. It's a typical example of formal English.
As for the meanings of the adjective "local" and the noun "locale", they are quite different. When we refer to something belonging to or connected with a particular place, we say it's a local thing. For example, I found the local people (or locals as a noun) very friendly, our local library is very small. I will have to go to another district for treatment as we don't have any local hospital for heart diseases, etc.
On the contrary, the noun "locale" is a place or site where something special happens or where the story of a book, film, etc. is set. For example, our city is full of interesting locales of recreational activities, our countryside is the only locale of our recreation, this movie was mostly set on the scenic locales of the country.