Nineteen of the Russian's 21 titles have been achieved on hard surfaces
A comeback the Russian player secured his first trophy for 882 days with success over opponent Moutet in the Almaty Open championship match.
The Russian, a ex- number one, has experienced a difficult season, managing just one match at the big events and undergoing a setback at the American major.
Medvedev's inconsistency on the tennis tour - and difficulties with his serve in especial - resulted in him falling of the elite rankings and finally splitting with former trainer his previous coach.
Presently working with Thomas Johansson and his other coach, he has steadily improved in the last few weeks - climaxing in a hard-fought three-set victory over challenger Moutet.
This marks Medvedev's maiden trophy after the 2023 Rome Masters and initial on a hard court from that period of the previous year.
Victory also signifies Medvedev has won twenty-one victories at twenty-one different competitions.
"This marks the first occasion I am participating in a event with my children at once, so to get a trophy is particularly special," commented tennis professional the champion.
"This title is in dedication of my child her name, because the first title I got when my older daughter my daughter was delivered was for her."
The athlete, the past champion, had been defeated in his previous six title deciders, featuring in Halle previously this season.
Medvedev's defensive approach and regular outbursts on the tennis court had caused observers to wonder if his capacity to play at the highest level was concluded.
But the athlete has altered his approach in recent weeks, striving to come to the net and play assertively, supported by an improved serve.
Medvedev recovered from a break down in the first set against the challenging Frenchman, taking four of the final five exchanges to gain the advantage.
Both players exchanged break points in the second set before Moutet, bidding for his initial professional title, seized the initiative to force a decider.
The opponent defended four initial opportunities in a competitive final set before the Russian secured a break to 15 to secure the win.
Suitably, the winner secured the title with a point at the net area, with his opponent failing to manage a return after two hours and 38 minutes.
