Nineteen of the Russian's 21 championships have been won on hard courts
A revitalized Medvedev claimed his maiden championship for 882 days with victory over opponent Moutet in the tournament championship match.
The athlete, a ex- world number one, has had a challenging period, managing just one match at the big events and undergoing a setback at the US Open.
Medvedev's varied form on the tennis tour - and difficulties with his service game in particular - led to him exiting of the world's top 10 and eventually splitting with long-term trainer his previous coach.
Currently working with his coach and Goetzke, he has steadily progressed in the past month - climaxing in a hard-fought 7-5 4-6 6-3 triumph over opponent Moutet.
This marks the player's maiden championship after the 2023 Rome Masters and initial on a hard court from March of 2023.
The win also means he has secured twenty-one championships at 21 various competitions.
"This marks the first occasion I have attended a event with my both daughters simultaneously, so to get a title is really nice," stated ranked player Medvedev.
"This title is in tribute of my younger daughter my daughter, because the first title I got when my child my daughter was born was for her."
Medvedev, the 2021 US Open champion, had been defeated in his previous six finals, including in that event previously this season.
The player's counter-punching approach and frequent reactions on court had led commentators to wonder if his capacity to play at the elite level was concluded.
But the 29-year-old has altered his approach in the past month, making an effort to approach the net and compete positively, backed up by an enhanced serving game.
The champion fought back from a deficit in the opening set against the tricky Moutet, securing four of the final five games to gain the advantage.
The pair exchanged breaks in the following set before the Frenchman, attempting for his initial tour title, took control to force a third set.
Moutet saved 4 initial chances in a close third set before the champion broke to fifteen to serve for the match.
Fittingly, Medvedev clinched the win with a point at the net, with his opponent failing to manage a shot after two hours and 38 minutes.
