A website was set up a week ago to gather signatures as part of a campaign that has now been widely publicised.
It comes after two of the leading candidates in this year’s election race have been hit by a series of scandals.
The website, called Obama2017.fr, said: “The French are ready to make radical choices. That is good because we have a radical idea to propose to them.
“Faced with the announced failure of the next presidential election, we think it is time to move to the 6th Republic to get France out of its lethargy.
“To launch this 6th Republic, we wish to strike a blow by electing a foreign President at the head of our beautiful country.
“Barack Obama has completed his second term as President of the United States on January 21, why not hire him as President for France?”
:: What you need to know about the French elections – and …