Celtic defender Gary Caldwell scored in the second half for the home side, giving Scotland three wins from three matches to go top of Group B in Euro 2008 qualifying after having also beaten the Faroe Islands and Lithuania.
"It's great for us to be at the top of the group," said Scotland manager Walter Smith.
"The hope before the group started was to do well in our first two games, which we did.
"I'm not so sure there was a great expectation for us to win against France but there is always a great deal of optimism in Scotland - that's just the way we are," Smith added.
"To take nine points from these three games is terrific and my hope is we can stay competitive right through the group."
France dominated the match at Hampden Park with Scotland goalkeeper Craig Gordon having a busy night behind a largely defensive set up for the home team.
However, Caldwell's goal from a Paul Hartley cross in the 67th minute stunned the French and secured a famous victory for the Scots who last beat France in 1989 on their way to the 1990 World Cup Finals.
Smith made no apologies for his side's defensive approach at home and praised his players for their great performance.
"It wasn't unexpected how much they dominated because of the qualities they have. It's no disrespect to anyone who plays for Scotland but anything we achieve will be through hard work," Smith said.
"Against the major teams like France we are happy to ride our luck at times and we deserved a bit of good fortune.
"Obviously I'm delighted that everything has fallen into place and we managed to get a fantastic win."
Domenech points the finger
France coach Raymond Domenech was disappointed with his side's efforts and even pointed the finger at the ball boys at Hampden Park after the shock loss.
"Scotland made a few loose passes and gave us a few balls but we were not fast enough to exploit the amount of possession we had," said Domenech.
Scotland's Darren Fletcher (L)
challenges France's Franck Ribery
"I knew before the game that this would be a difficult game and I tried to warn the players. Scotland will be a big threat to the other teams in this group."
"But I was disappointed with the attitude of the ball boys who slowed the game down whenever the ball went out of play," added Domenech.
"That was very disappointing for me from a country known for their fair play."
Scotland now travel to Kiev to play Ukraine on Wednesday, who went down 2-0 to Italy on Saturday thanks to a Massimo Oddo penalty in the 71st minute, and a Luca Toni goal in the 79th minute.
France return home to Sochaux on Wednesday where they take on the Faroe Islands, who suffered an unlucky 1-0 loss to Lithuania after Andrius Skerla stole the points with an 89th minute goal.
England disappointed and frustrated
Meanwhile in Manchester, an under par England shared the points with Macedonia, failing to capitalise on home ground advantage against a team they had defeated 1-0 in Skopje last month.
New England manager Steve McClaren suffered his first set back after winning his first two matches in charge.
England's Steven Gerrard (L) vies
with Goran Maznov of Macedonia
"I am disappointed and frustrated, and so are the players in the changing room," said McClaren.
"Looking at the performance it has got to be better."
England midfielder Steven Gerrard hit the crossbar in the 85th minute, but that was as close as England got on a night where they failed to fire.
Gerrard also picked up his second yellow card in as many matches and will miss England's game against Croatia in Zagreb on Wednesday.
"It's a big blow for us to lose Stevie," McClaren said.
"With Steven missing, we are now going to have look at the situation and reflect on what we are going to do tactically."
Macedonia coach Srecko Katanec said that he expected more from England after their encounter in Skopje last month.
"I expected England to play a more aggressive game and put us under more pressure," Katanec said.
"But I am very satisfied with the performance of my players because they played well tactically and earned a very good point."
Macedonia now play Andorra who were thrashed 7-0 in Croatia with Basel striker Mladen Petric scoring the first four goals of the match.
In other results, Cyprus stunned Ireland winning 5-2 at home, while the Czech Republic beat San Marino 7-0.
Denmark drew 0-0 with Northern Ireland, and Sweden surprised Spain by winning 2-0 at home.