Industrial-Organizational Psychology & HR Consulting
I was a full time psychology faculty member at a small, private university for 10 years. My school had a very strong pre-med program with advisors for those students with medical school aspirations. While many pre-med students pursue biology or biochemistry majors for medical school, psychology majors are also competitive for medical school.
FYI: The Medical College Admissions Test (MCAT) now includes a section on the behavioral sciences. Therefore a psychology major will definitely assist you in performing well on the MCAT.!
Regarding your question about a double major: I generally encourage double majoring especially in another language as it helps develop the brain AND makes the student more desirable for professional and post graduate studies AND employment. However, you will be required to take additional coursework in the sciences for pre-med that go beyond the coursework for the psychology major. That is an additional course every semester! You just might be over loaded with a double major.
Be sure to apply to universities with a strong placement rate for its pre-med students! Good luck with your academic pursuits.