A first-half goal from Georginio Wijnaldum and Memphis Depay's penalty deep into injury time earned the Oranje a convincing victory over the World Cup winners at De Kuip in Rotterdam.
Netherlands missed out on qualification for the tournament in Russia, having also failed to make it to Euro 2016.
But signs of recovery are seemingly emerging, leaving Koeman optimistic.
"I did not expect that we would be the better team for ninety minutes," he told Dutch broadcaster NOS.
"I also did not expect to be able to read the whole match so well. I am proud of this mature performance against France.
"This is a huge step. We talk about it every time, that next step. Now we have seen a match in which we, even against an opponent like France, start well and hold on to the end.
"In one or two moments, we took a little too much risk in putting pressure on, but we had 12 goal attempts and France two. We already had opportunities at 2-0. Their keeper was great, otherwise it would have been 3-0 or 4-0. That could have happened. It is exceptionally good what the players have shown tonight."
Koeman hailed the renewed enthusiasm of his side, as they seek to drag the national team back onto the big stage at Euro 2020.
"You see it a lot, at training sessions and during competitions, how self-consciously the group is working to get better and to achieve success, something that has not happened for a number of years," he said.
"And then also in this type of game. We now have six points and chance a to win. Nobody expected that, nor did I. This gives a team so much confidence."
Just five months after watching Les Bleus reach the pinnacle of the sport by winning the World Cup, France coach Didier Deschamps acknowledged they were second best on Friday.
"There was a team in front of us with a lot of envy and we were not good enough," Deschamps was quoted as saying on the French Football Federation website.
"There was no picture in attack tonight and it's logical that this Netherlands team wins this match.
"And I do not exclude myself from this analysis.
"We're not going to take refuge behind absences, [playing at] the highest level has requirements and we did not meet them.
"We had too much technical waste."