Telemedicine is often put forward as a solution to medical deserts. Recently, telemedicine has allowed to limit physical contacts during a pandemic. We analyze within a theoretical model the setting of physicians' fees in the presence of distant medicine and public health insurance, as well as the resulting patients' surplus, access and public expenses. Concretely, we consider that distant medicine is provided either by the same physician as in-person medicine or by another one specialized in distant medicine. We compare the outcomes of these two market structures with each other and with a benchmark monopoly with no distant medicine. This comparison allows to discuss the effects of a recent French reform concerning insurance reimbursements for distant medicine, as well as those of cross-border high-quality remote health services.