Best and Sexton both went over in the first half as Ireland opened up a 19-0 lead at the break, Jack Conan also crossing.
While Les Bleus scored two late tries, this was a controlled performance from the Irish, who secured the bonus point and stay in contention for the Championship.
Joe Schmidt’s side will now go to Cardiff to take on Grand Slam-chasing Wales in Round Five, trailing the Welsh by two points.
Their title hopes are not in their hands, with England sandwiched in between the two sides, but Schmidt at least has a chance of a Championship in his final campaign.
The first half was dominated from start to finish by Ireland, running in three tries and with nearly 90 percent territory.
Full Time score: IRELAND 26-14 France #TeamOfUs #IREvFRA #ShoulderToShoulder pic.twitter.com/omPh8EUi4Q
— Irish Rugby (@IrishRugby) March 10, 2019
Best got the ball rolling just three minutes in from a lineout maul, before Sexton and Conan both crossed in quick succession.
Another Lion in Keith Earls added the fourth just before the hour, and despite late tries from Yoann Huget and Camille Chat, the result was never in doubt.
And after the game Ireland skipper Best said: “I think the way we controlled the game when you look at it as a whole, we are very happy with.
“We had a lot of chances that we could have put away earlier but you can’t underestimate how good and physical that French team is.
“We probably weren’t expecting to get as many lineouts we did but we had a few plans in place and few came off but also a few didn’t.
“We know that going to Cardiff next weekend they are going to be in fantastic form and we have only a six day turnaround and a lot of sore bodies.”
