Nineteen of Medvedev's 21 titles have been won on hard courts
A comeback the Russian player won his maiden championship for over two years with a win over opponent Moutet in the Almaty Open title decider.
Medvedev, a former number one, has had a difficult season, achieving just one match at the Grand Slams and suffering a meltdown at the US Open.
His unpredictability on the professional circuit - and difficulties with his service game in specific - led to him falling of the top ten and eventually splitting with long-time coach his previous coach.
Now training with his coach and Rohan Goetzke, Medvedev has consistently progressed in the past month - peaking in a hard-fought competitive triumph over opponent Moutet.
It is the player's first title since the Rome competition and maiden on a hardcourt after that period of 2023.
Victory also signifies Medvedev has achieved 21 championships at 21 distinct events.
"This marks the first occasion I'm at a competition with my both daughters together, so to secure a trophy is particularly special," said tennis professional the champion.
"This title is in tribute of my child Victoria, because the initial championship I got when my child Alisa was born was for her."
The tennis star, the 2021 US Open champion, had failed in his last six title deciders, featuring in that event previously this season.
The player's counter-punching approach and regular reactions on the tennis court had led observers to doubt if his capacity to play at the top level was concluded.
However the athlete has made changes in recent weeks, striving to come to the net and compete aggressively, backed up by an improved serving game.
The champion fought back from a deficit in the initial set against the challenging opponent, taking four of the last five exchanges to take the lead.
The competitors traded break points in the following set before Moutet, bidding for his maiden tour victory, gained dominance to create a final set.
He defended 4 early chances in a competitive deciding set before the Russian secured a break to that score to secure the win.
Appropriately, he clinched the win with a shot at the front of the court, with the Frenchman unable to manage a shot after a lengthy match.
