Without getting too political, I wonder if this is a case where the doctor is not allowed to set market price for his/her services therefore he can not afford to live on the island. I am sure it's a mix of this and other things forcing the decision to leave.
Who would set the price for his/her services, and are his/her prices set at the same rate as a pediatrician in France?
Also, who pays for the medical expenses for the many travelers from the US? Is this something that the French government pays for or the patient pays for with their medical insurance (I am guessing it's the former)?