They should have a choice: go to Saint-Pierre and Miquelon or go home, said Republican Wauquiez on Tuesday to the right-wing website JD News.
Saint-Pierre and Miquelon is a French self-governing island group off the coast of Canadian Newfoundland. The windswept islands have a population of less than 6,000 people.
Wauquiez, a member of parliament and former party leader of the conservative Republicans (LR), hopes that the island group's climate will have a "deterrent effect" on migrants.
The average temperature is five degrees and they have rain and snow 146 days a year. I believe that it would fairly quickly make everyone think twice.
The proposal has sparked criticism across French party lines.
Forced exile is a settler method, not a method for an elected legislator, says Manuel Valls, minister for France's overseas territories from President Emmanuel Macron's party Renaissance.
Boris Vallaud, leader of France's socialist parliamentary group, describes Wauquiez's "shameful and idiotic" proposal as a "sea-Guantánamo". Even convicted far-right politician Marine Le Pen criticizes the idea.