19 of Medvedev's twenty-one victories have been earned on hard courts
A resurgent the Russian player secured his first championship for 882 days with success over opponent Moutet in the Almaty Open final.
Medvedev, a ex- world number one, has had a difficult season, managing just one match at the Grand Slams and suffering a difficult moment at the New York tournament.
His inconsistency on the ATP Tour - and issues with his serving in particular - resulted in him exiting of the top ten and finally parting ways with long-time mentor Gilles Cervara.
Now collaborating with Thomas Johansson and Rohan Goetzke, Medvedev has gradually progressed in the past month - culminating in a closely contested three-set victory over Frenchman Moutet.
This represents the player's first championship after the 2023 Rome Masters and initial on a hard court since that period of that year.
Victory also indicates Medvedev has secured 21 titles at twenty-one various events.
"It's the first time I am participating in a event with my children simultaneously, so to secure a title is really nice," commented world number 14 Daniil Medvedev.
"This title is in honour of my second daughter her name, because the initial championship I achieved when my first daughter her name was born was for her."
Medvedev, the 2021 US Open champion, had lost his last six championship matches, comprising in Halle earlier this year.
His counter-punching strategy and regular emotional displays on the tennis court had caused commentators to doubt if his skill to perform at the highest level was over.
However the athlete has altered his approach in recent weeks, making an effort to approach the net and compete aggressively, reinforced by an enhanced service.
He fought back from a break down in the initial set against the challenging opponent, winning 4 of the last five points to gain the advantage.
The competitors traded break points in the middle set before the Frenchman, attempting for his initial ATP Tour championship, took control to push for a third set.
He saved 4 initial chances in a close third set before Medvedev secured a break to 15 to close out the victory.
Appropriately, the winner earned victory with a rally at the net area, with his opponent unable to manage a volley after over two and a half hours.