After promising performances in narrow defeats against Australia and New Zealand last November and against England last weekend, Les Bleus put on an untidy display at the Stade de France with flyhalf Camille Lopez kicking 17 points in their 22-16 victory.
Scotland's tries came from star fullback Stuart Hogg in the first half - his third of the tournament - and lock Tim Swinson's effort after the break.
Scotland beat Ireland in their first Six Nations game, but could only claim a bonus point eight days later after they were overpowered by Guy Noves' powerful side and came away with captain Greig Laidlaw on crutches and wearing a protective boot on his right foot.
Scotland have never won an RBS Six Nations Championship match in Paris but, having broken their opening-match hoodoo after 11 years' of trying, he says they are determined to crack another. "I think we chucked it away at the end", Hogg said.
"(It's difficult) when you lose your captain and playmaker", Cotter said.
"We want to construct tries with the quality of our attacking game and put them under pressure with our defence, and being good both sides of the ball".
"But, we didn't look after the ball, we didn't respect it enough and ultimately that has cost us". "Obviously they've got big players, a big pack, so it was pretty bruising". We couldn't get rhythm into our attack.
"We want to be in control of our own destiny, we want to win or lose the game by the quality of our own performance, not turning up and relying on the opposition playing poorly to sneak a few penalties or maybe some sort of intercept try or turnover with our defence", said the former All Black global. We made a lot of mistakes in the first half, but we desperately needed the win.
Hogg is set to become the 40th Scotland player to reach a half century of caps and, at 24 years and 233 days at kick off, will break the record now held by teammate Richie Gray, who made his 50th appearance at 26 during the 2015 World Cup. "We were in the lead and definitely in a position to win - so everyone is disappointed because we could have won it".
Hogg and Scott Spedding both missed penalties while France nearly scored a second try on 67 minutes but Remi Lamerat was deemed to have failed to have grounded the ball following a try review.
"But we've also got to be careful when doing it, because if you get it wrong or they sniff an opportunity where you're a little disconnected, they're one of the best at taking advantage".
"It's tough going out there", Hogg said on BBC One. "We are really lucky just to sneak away at the end there". We weren't looking after it.