Tim Swinson also crossed for his first global try to put Scotland 16-13 up just after the break, but 17 points from the boot of the impressive Camille Lopez and a Gael Fickou try in the second half gave Les Bleus their first win of the tournament.
Scotland lost four players to injury during the course of the match at the Stade de France, starting with captain and first-choice kicker Greig Laidlaw with an ankle problem after just 25 minutes.
And while Scotland did at least claim a losing bonus point, Cotter admitted his team had struggled to impose their game plan because of the pressure put on them by France.
Scarlets loose forward forward John Barclay replaced the injured Ryan Wilson in the only change to the Scotland team announced on Friday for Sunday's Six Nations clash with France in Paris. "That's why everyone is talking about the resurgence in French rugby and I think they are getting back that flair that everyone likes to see from them".
"(It's difficult) when you lose your captain and playmaker", Cotter said.
France played much better against England, but this game was about resilience and finding enough grit to grind out a win.
"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. We didn't look after the ball, didn't respect it, and ultimately that's cost us".
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His unhappiness was on display when he tweeted, after the call with Mr Turnbull , that "I will study this dumb deal". I find that both un-American and un-Australian, a choice that destroys any faith I had in Turnbull's integrity.
"But in those previous games, they probably were still fighting against the way management wanted them to play, but now that they've been given this license and they're confident in what they do, we need to be really disciplined.
But we weren't ideal", Scotland prop Zander Fagerson said.
"A win against them is hugely important because we now know we can compete with the very best, which is something we believed anyway but needed to prove. There are other bumps and bruises but we are hoping everyone will be alright for the next one".
"There's no reason whatsoever we can't go over to Paris and get a win".
"The players showed a lot of courage not to take a try in the last 10 minutes on our line".
Having gone behind to aCamille Lopezpenalty, Stuart Hogg, who crossed twice in the triumph over the Irish eight days ago, was on the end of a fine move to go over in the corner for his third try of the Championship to give the visitors an early lead. They got six points clear and it was going to be tough from there. The second came just before the half and from a long way out, making the score 13-11. We weren't looking after it. Conversions must be completed within 90 seconds of a try being scored.