You can take the pre-med courses (biology, chemistry, organic chemistry, biochemistry, physics) alongside a CS major. Pre-med courses in math will likely be included in the CS major, and those in English composition and social studies could be overlapped with college general education requirements.
It will likely be easier to fit pre-med courses into a CS major schedule if the CS major is not engineering-based.
Because most pre-meds either drop out of pre-med or (if they apply) do not get into any medical school, pre-meds should consider their choice of major in the context of their backup plan, which is the most likely outcome. Biology majors do not have particularly good major-related job and career prospects at the BA/BS level.
Also, if you do go to medical school and do not have wealthy generous parents, you need to consider what your financial plan will be to pay off what could be $400,000 in medical school debt – for many physicians, this can take decades, even on physician pay, unless they continue to spend on a student budget.