Brian
I am not familiar with hunting opportunities in Alsace, but can give some general information on hunting for non-French residents.
Short-term (9 day) hunting licenses can be purchased by non-residents. They require purchasing insurance, paying fees to hunting organisations, showing passports, presenting photos, and most importantly for an advance planning point of view, presentation of your hunting license from your home country.
If you wanted, I could e-mail you a copy of more detailed information (in French) from a French source. I would not trust the accuracy or completness of my translation.
Leonard