"Oui on peut!"
The slogan on posters in Paris streets translates as "Yes We Can!"
Heard that before?
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Their online petition has already attracted more than 45,000 signatures in 10 days and they hope to reach a million supporters by March 15.
With the buildup to the April-May presidential election so far dominated by the corruption investigation targeting conservative Francois Fillon, organisers say they want to inject a dose of humour in the campaign.
Though widely popular in France, Obama has no chance of success. He is not French and has no right to take part in the race.
Sarah Wachter, an American who has lived in France since 1999, sees the petition as a positive sign for France.
"People want change but they want the right kind of change. Change that is inclusive, change that is human but change that is also open to the world and that is a very delicate balance to strike," she told AP. "But I think that Obama has done that in the United States.
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