Ireland scored three first-half tries with Hugo Keenan, James Lowe and Andrew Porter all crossing.
Damian Penaud's brilliant counter-attacking try and three Thomas Ramos penalties kept France in touch.
Ramos cancelled out Ross Byrne's penalty with a drop-goal, but Garry Ringrose's try secured Ireland's win.
The victory further underlines Ireland's status as the world's number one side and gives Andy Farrell's side a national record 13th straight home win, while ending France's dream of a second successive Grand Slam.
Having taken bonus-point wins over Wales and France, Ireland will next face Italy in Rome on 25 February with France hosting Scotland a day later.
Saturday's match had been billed as a titanic showdown between the championship favourites and it comfortably met the hype as the world's top two sides produced an electrifying first-half spectacle.
While France took an early lead through Ramos' fifth-minute penalty, Ireland immediately set about regaining control and, while Andrew Porter was denied a try in the hosts' opening attack, Finlay Bealham's sleight of hand sent Keenan scything through before crashing over for a well-worked score.
However, after a second Ramos penalty cut Ireland's lead to a single point, France ruthlessly exploited space in the home side's defence when Anthony Jelonch rampaged through Irish bodies and fed Penaud, who sprinted clear to finish off a stunning counter.
With most of the stadium still marvelling at Penaud's score, Ireland worked the ball out to Lowe who, despite Penaud's attempts to push him into touch, acrobatically managed to touch the ball down in the corner, with the try standing following a lengthy TMO review.
Sexton's failed conversion attempt meant Ireland trailed 13-12, but after Uini Atonio was yellow-carded for a high hit on Rob Herring, Porter marked his 50th cap by scoring Ireland's third try before Sexton's penalty put the hosts six points clear at the end of a breathless opening 40 minutes.