19 of Medvedev's twenty-one titles have been won on hard courts
A resurgent the Russian player secured his first trophy for nearly 30 months with victory over opponent Moutet in the Almaty Open championship match.
Medvedev, a ex- number one, has had a challenging period, winning just one win at the major tournaments and suffering a difficult moment at the American major.
The player's inconsistency on the tennis tour - and issues with his service game in especial - caused him exiting of the elite rankings and ultimately separating with former coach his previous coach.
Now working with Thomas Johansson and his other coach, he has steadily progressed in the last few weeks - climaxing in a tightly fought 7-5 4-6 6-3 triumph over challenger Moutet.
It is the player's maiden trophy following the 2023 Rome Masters and initial on a hardcourt since March of the previous year.
Success also signifies Medvedev has secured twenty-one championships at twenty-one various tournaments.
"It's the first time I have attended a event with my children together, so to get a trophy is especially meaningful," commented world number 14 Medvedev.
"This victory is in honour of my younger daughter my daughter, because the initial championship I got when my first daughter her name was born was for her."
Medvedev, the former major winner, had failed in his last six finals, including in that event earlier this year.
Medvedev's defensive strategy and frequent outbursts on court had caused observers to question if his skill to play at the top level was over.
But the 29-year-old has made changes in recent weeks, attempting to come to the net and perform aggressively, reinforced by an enhanced service.
Medvedev recovered from a break down in the initial set against the challenging opponent, winning 4 of the concluding five points to go ahead.
The competitors traded breaks in the middle set before the Frenchman, attempting for his first ATP Tour victory, gained dominance to push for a final set.
Moutet saved 4 early break points in a tight final set before the Russian broke to fifteen to serve for the match.
Fittingly, the winner earned the win with a shot at the net area, with Moutet incapable to handle a shot after a lengthy match.