Nineteen of Medvedev's 21 titles have been achieved on hardcourt
A resurgent the Russian player claimed his maiden championship for over two years with success over opponent Moutet in the tournament championship match.
The Russian, a ex- number one, has experienced a challenging season, managing just a single victory at the Grand Slams and experiencing a difficult moment at the New York tournament.
The player's inconsistency on the ATP Tour - and difficulties with his serve in especial - led to him dropping out of the world's top 10 and ultimately splitting with long-term trainer Gilles Cervara.
Now training with Johansson and Goetzke, he has consistently improved in the recent weeks - climaxing in a closely contested three-set win over Frenchman Moutet.
It is Medvedev's initial title after the 2023 Rome Masters and initial on a hard court from that period of that year.
Success also signifies he has secured twenty-one titles at 21 various events.
"This marks the first occasion I have attended a tournament with my children at once, so to secure a trophy is really nice," said world number 14 Medvedev.
"This title is in honour of my second daughter Victoria, because the first title I got when my first daughter her name was born was for her."
Medvedev, the past champion, had been defeated in his last six championship matches, comprising in Halle previously this season.
His counter-punching approach and recurring outbursts on the tennis court had led some to wonder if his capacity to play at the highest level was over.
However the 29-year-old has made changes in the last few weeks, striving to come to the net and play aggressively, reinforced by an enhanced serve.
The champion fought back from a deficit in the first set against the challenging Frenchman, taking 4 of the last five points to gain the advantage.
The pair swapped breaks in the middle set before the Frenchman, attempting for his initial professional title, seized the initiative to push for a final set.
Moutet defended four initial break points in a competitive final set before the champion broke to that score to secure the win.
Appropriately, he earned the win with a rally at the net area, with the Frenchman incapable to manage a return after two hours and 38 minutes.
