Ireland must next go to Cardiff to take on Wales, beaten on Saturday by Scotland, on Friday, March 10 before welcoming defending champions England, who will be expected to stretch their unbeaten record in the 2017 tournament to three from three when they welcome Italy to Twickenham on Sunday.

IRTV: Ireland post-match press conference #IREvFRA #TeamOfUs https://t.co/ZL2MI0qbaw

— Irish Rugby (@IrishRugby) February 25, 2017

Ireland's title destiny is still in their own hands and Schmidt said: “One of the key things is that England are going to keep going full speed and I think Scotland (their fourth round opponents) have proven that they're very difficult to get past and losing (scrum-half and captain) Greig Laidlaw is a big blow for them. They stuck at their task today and they are going to go fully armed to Twickenham.

“I think the Championship is super. I saw some basketball results this morning (in Super Rugby) and there's not too many of those. It is massively intense and it has certainly coaches on the edge of our seats and players working incredibly hard to make sure that they deliver as best they can.”

Schmidt was delighted with a 10-point winning margin that is Ireland's highest over the French since the championship became the Six Nations in 2000. They recovered from a shaky start that saw them go 6-0 down to two Camile Lopez penalties before man-of-the-match Murray's converted try gave the home side a 7-6 half-time lead. Sexton, playing his first rugby since a calf strain on January 20 took over after the break, slotting a penalty and the drop goal before his replacement Paddy Jackson slotted the penalty that denied France a losing bonus point.

“It was a performance that I suppose I've got a fair bit of admiration for the players, they've really had to roll their sleeves up. Conditions were really tough, even early in the game when there wasn't as much drizzle it was still wet and slippery, hard to get your feet on the ground, hard to control the ball but I thought we did pretty good job of it.

“Unfortunately we let that slip a few times and fell behind on the scoreboard but I was really impressed with the way the players knuckled down and worked their way back into the game. We got the try we needed to give ourselves the confidence that we could continue to build and keep the pressure on and that's what they did.”

Schmidt said Sexton's return from injury had made a big impact on Ireland.

“I thought he was really really positive for us. It's based on experience. It's certainly not the first time that Johnny's done it. He tends to come in and prepares himself incredibly well. He's got such a competitive edge that he wants to be at his best, and he actually felt good, he felt fresh. For some of the other players, because you accumulate a few knocks and fatigue week to week Johnny came in feeling pretty good.

“The game was a little bit stop-start, even though there were long periods of play, it was stop-start at the scrums, for instance, resets, the bits of the game that are probably frustrating for everyone including us that at least probably allowed him a bit of a breather as well.”

Rob Kearney was the only injury concern, the full-back withdrawn early in the second half after experiencing discomfort in his adductor and Ireland's medical staff will wait to properly assess whether he will be fit to face Wales on March 10.