In wet conditions at the Stade de France they had the better of the first half, going in at half-time six points to the good thanks to two Greig Laidlaw penalties.
Les Bleus responded with three penalties to lead for the first time, and although Laidlaw got the Scots back on level terms, two quick tries from Wesley Fofana and Maxime Médard just after the hour, turned the tide decisively.
Tim Visser hit back for the Scots late on, and Hamilton insists there are positives to take from the tournament as a whole despite the defeat in Paris.
He said: "Naturally we are pretty disappointed, we thought we could come here and win and that was our mindset going into the game.
"Up to 60 minutes we were definitely in the game and then the tide turned a bit, we dropped off a few tackles, they probably got a bit of dominance in the scrum and that was probably the turning point.
"We've got to take a lot out of that. We have had a half-decent tournament, our defence has been outstanding at times, we've dug deep and we are team that never give up.
"We've got a lot to work on and we just want to get better every time we play.
"We are on an upward curve, we've always said we are trying to learn, we've got new guys in the team, we have got a few young guys who are stepping up and doing well.
"There is still a lot of work to do, we've got a big tour in the summer and we are just looking to improve every time we play."