Vichot outsprinted Jose Joaquin Rojas Gil and Cyril Gautier on the Promenade des Anglais to finish the 128-kilometer trek around Nice in 3 hours, 06 minutes, 56 seconds.
In the overall standings, Betancur was 14 seconds ahead of world champion Rui Costa, who crashed in the final straight. Vichot placed third, 20 seconds behind Betancur.
Betancur won two stages in the week-long race. He finished fifth in last year's Giro d'Italia.
Earlier Sunday, Frank Schleck and Simon Spilak broke away from the pack on the ascent of Col d'Eze but were caught in the last kilometer.
Geraint Thomas and Edvald Boasson Hagen were among the riders who did not start the stage. Thomas was a contender for the race victory but suffered a late crash in Saturday's stage. Team Sky said Thomas "should return" for the Milan-San Remo race on March 23.
Tom Boonen, Tyler Farrar and Thomas Voeckler were among the riders to drop out early in the stage that featured five climbs.