A dejected McGeechan said: "We said last week that scoring six points against Ireland wasn't good enough at home and today not being able to cross France's line when we had one or two opportunities was very disappointing.
"You've got to be looking to score 15-20 points if you want to win matches but today we could not finish our chances.
"In parts of the game where you have have to build control - especially away from home - we were lacking. We had opportunities but we're not reacting well when we do break the line.
"The ball-carriers were trying to make the links - when you get behind the line you want to buy time but we didn't do that."
McGeechan refused to look too closely at the championship table, instead choosing to focus on his side's next match against Wales at Murrayfield in two weeks' time.
"We'll have to wait and see if the championship table splits into two parts," he said.
"We just want to be competitive against Wales and we'll see what happens. We'll certainly work very hard at being competitive the next time we turn up."