"Environment" VS "Milieu"

I see no difference between “environment” and “milieu” in the following example:

• It is a study of the social and cultural milieu in which Michelangelo lived and worked. [Source]

I think, we can interchange the two words here in this example.

As Cambridge says, “milieu” is:

The people, physical, and social conditions and events that provide the environment in which someone acts or lives.

This is my exact definition of “environment”.

Are they interchangeable in this sense?
Should I consider any point here?