Nineteen of Medvedev's 21 titles have been achieved on hard surfaces
A revitalized the Russian player secured his maiden title for nearly 30 months with victory over opponent Moutet in the tournament championship match.
The Russian, a ex- number one, has experienced a difficult period, managing just a single victory at the Grand Slams and suffering a meltdown at the American major.
The player's unpredictability on the ATP Tour - and difficulties with his service game in particular - led to him falling of the world's top 10 and finally separating with former coach Cervara.
Now training with Thomas Johansson and Rohan Goetzke, the tennis star has consistently progressed in the recent weeks - climaxing in a tightly fought 7-5 4-6 6-3 win over opponent Moutet.
This represents the player's first championship since the 2023 Rome Masters and initial on a hardcourt after March of 2023.
Success also signifies the Russian has secured twenty-one championships at twenty-one distinct competitions.
"It's the first time I'm at a competition with my both daughters together, so to secure a trophy is particularly special," said world number 14 Medvedev.
"This title is in tribute of my younger daughter my daughter, because the first title I won when my first daughter Alisa was born was for her."
Medvedev, the 2021 US Open champion, had lost his past six finals, featuring in Halle earlier this year.
His retrieving approach and recurring emotional displays on court had led some to question if his skill to compete at the highest level was concluded.
However the player has altered his approach in the last few weeks, striving to advance forward and perform positively, reinforced by an better service.
The champion came back from a disadvantage in the initial set against the difficult opponent, securing 4 of the concluding five games to gain the advantage.
The competitors exchanged break points in the second set before the challenger, striving for his first ATP Tour title, took control to create a third set.
He defended 4 early chances in a competitive third set before the champion broke to 15 to close out the victory.
Fittingly, Medvedev earned the win with a rally at the net, with the Frenchman unable to control a volley after two hours and 38 minutes.