The winner of the day's final stage was France's Arthur Vichot, who outsprinted Spain's Jose Joaquin Rojas and compatriot Cyril Gautier to cross the line first having come close several times this week.
The 24-year-old Betancur, who joined the AG2r-La Mondiale outfit last season, kept his composure in Sunday's 128-km ride around Nice.
It was the first victory by a French team in the Paris-Nice since Toshiba dominated the field with Swiss Tony Rominger in 1991.
"It had been 23 years without an overall win for a French team here and my team is 23 years old," team manager Vincent Lavenu told reporters.
"It is important that a French team win this first big World Tour event."
Betancur was able to count on team mates Mickael Cherel, Romain Bardet and Alexis Vuillermoz throughout the race.
In the finale, Luxembourg's Frank Schleck and Slovenia's Simon Spilak tried their luck but were reined in with the finish line in sight.
World champion Rui Costa of Portugal, second overall and 14 seconds off the pace, crashed heavily as the peloton got nervous with the final sprint looming.
He got back on his bike and was credited with the peloton's time as his accident happened within the final three kilometres.
Vichot, who confirmed he has a bright future with the stage victory, took third place overall 20 seconds behind Betancur.
"I could not dream better. It's fantastic to win with the (French champion's) red, white and blue jersey," Vichot told reporters.
"It's a reward for the team as well, they have been working hard all week."
Betancur, who was thrust into the limelight last season after finishing fifth in the Giro, third in the Fleche Wallonne and fourth in the Liege-Bastigne-Liege, seized the Paris-Nice lead on Friday with his second stage win of the week.
Britain's Geraint Thomas, who wore the overall leader's yellow jersey early on, pulled out of the race on Sunday after sustaining injuries in a crash on Saturday.
Team Sky said he would be fit for next weekend's Milan-San Remo classic.
- Sports & Recreation
- Arthur Vichot
- Jose Joaquin Rojas
- Cyril Gautier