19 of Medvedev's twenty-one championships have been achieved on hard surfaces
A comeback the Russian player secured his first trophy for over two years with a win over opponent Moutet in the Almaty Open final.
Medvedev, a ex- world number one, has had a difficult season, managing just a single victory at the big events and undergoing a setback at the American major.
Medvedev's varied form on the ATP Tour - and struggles with his serving in particular - led to him exiting of the world's top 10 and eventually splitting with long-term mentor his previous coach.
Currently training with Thomas Johansson and Rohan Goetzke, the tennis star has gradually improved in the last few weeks - peaking in a tightly fought competitive win over challenger Moutet.
It is the player's first title since the 2023 Rome Masters and initial on a hard surface since spring of the previous year.
Victory also signifies he has achieved twenty-one titles at 21 distinct events.
"It's the first time I am participating in a competition with my children simultaneously, so to win a championship is especially meaningful," said ranked player Daniil Medvedev.
"This championship is in tribute of my child her name, because the initial championship I achieved when my child Alisa was born was for her."
The athlete, the past champion, had failed in his previous six title deciders, featuring in that event earlier this year.
Medvedev's defensive strategy and frequent outbursts on court had led some to question if his skill to play at the elite level was finished.
Yet the athlete has made changes in recent weeks, striving to come to the net and play assertively, reinforced by an better serve.
The champion fought back from a break down in the initial set against the tricky Moutet, securing 4 of the last five games to go ahead.
Both players exchanged service breaks in the following set before the Frenchman, attempting for his initial tour championship, took control to force a third set.
Moutet defended four early opportunities in a close third set before the Russian broke to 15 to serve for the match.
Suitably, Medvedev secured victory with a point at the front of the court, with Moutet unable to control a return after over two and a half hours.
