Scotland captain Greig Laidlaw wants one more "huge effort" from his team to win a third straight game and match their best Six Nations campaign.
Beating Ireland in Dublin next Saturday would equal Scotland's three wins of 2006, and likely secure third place.
"It will be a tough game but we are determined to finish the competition well," Laidlaw told BBC Scotland.
"Ireland are a good side and it is going to take one huge effort to try to get what would be a massive win."
Sunday was a special day for Laidlaw, who celebrated his 50th cap by equalling David Sole's record of leading Scotland in 25 Tests.
"To lead this team out at Murrayfield is something that will stay with me forever," he said.
"But it is not about individuals. The whole team and the crowd were literally as one today. It was outstanding."
Horne 'fitted in brilliantly'
Scotland suffered the early setback of losing fly-half Finn Russell to a head knock after just five minutes, in the build-up to France's opening try.
But Laidlaw paid tribute to his replacement Peter Horne, usually a centre and who has only started one Test at stand-off.
"Peter deserves enormous credit," he said. "I thought he was fantastic when he came on. He's probably not played a huge amount of rugby there but he fitted in brilliantly and made it as smooth as possible for the team.
"I thought we scored a couple of great tries in amongst some very gritty defence. France put a lot of width on the game at times and we really had to scramble at times and fought for each other. You could see how much it meant to us all."
Scotland were inspired by full-back Stuart Hogg, who scored their opening try, landed a penalty from inside his own half and created the clinching try for Tim Visser with a wonderful overhead pass.
"When we lost Finn, everyone stepped up but Hoggy was great," acknowledged coach Vern Cotter.
"It was nice to see that chemistry among the players. There was constant talking and encouragement and the positivity on the field was great.
"The players adapted well when Finn went off, there was no panic in the ranks. It was nice to see a composed team believing in its strengths and eeking out a win.
"The guys are a humble bunch and they will enjoy this, but they know there is another game to come."
Practice makes perfect
Man-of-the-match Hogg admitted to a "wee bit of luck" in his assist for Visser's try, but believes hard work on the training ground is reaping its rewards.
Scotland's three tries took their tally for this year's Championship to eight, their best since scoring eight in 2005 and one fewer than their best tally of nine in 2000.
"You don't get many opportunities in international rugby and the ones we have created we have finished them off," he told BBC Sport.
"We have worked hard in training on that and it is great to see that coming off in the game.
"The team worked incredibly hard during the week to get that victory. You could see how much it meant to us in front of our home crowd. They were unbelievable.
"We can look forward to going to Ireland next week now."
|Analysis - Former Scotland captain Andy Nicol:|
|"What has been satisfying from Scotland's perspective is they have got better with each game of the Six Nations. It was a slow start against England, but they got better in Cardiff, better again in Rome and this was the best performance of the Six Nations so far. There were stand-out displays from Stuart Hogg, Richie Gray, John Hardie, but collectively there was a real togetherness and an understanding of how to play and a desire to do it. It was a very good performance and they fully deserved the victory."|