In the US, professor (or instructor) or advisor are probably most common for promoteur. Sponsor also sounds appropriate, and might be used as well.
An internship is usually a special kind of course. So it has an instructor or professor.
An example from Univ of CA, San Diego uses faculty supervisor:
The Academic Internship Program is a Special Studies Course, AIP 197. As such, a faculty advisor is required for all students participating in an AIP internship. Faculty Advisors help students create a structure to investigate a particular research question related to the internship, and guide students in developing a paper or project to address their research interest.
In my experience supervisor is used for Maître de stage. And that's true for the example program I referenced above:
AIP is an academic program, so participating organizations must adhere to the policies and procedures outlined in AIP's Supervisor Guidelines.
I worked as a university administrator for a couple of years, so I base this on some professional experience. I also know that different countries, schools, and companies/employers will use different terms.