19 of the Russian's twenty-one championships have been achieved on hardcourt
A resurgent Medvedev won his first title for 882 days with success over Frenchman Moutet in the competition final.
Medvedev, a former number one, has experienced a torrid period, achieving just a single victory at the Grand Slams and undergoing a setback at the American major.
Medvedev's inconsistency on the tennis tour - and difficulties with his serving in specific - caused him falling of the top ten and finally separating with long-term mentor Gilles Cervara.
Now collaborating with his coach and Goetzke, he has steadily improved in the recent weeks - peaking in a hard-fought three-set victory over challenger Moutet.
It is his first trophy following the 2023 Rome Masters and maiden on a hard court from that period of 2023.
Victory also signifies Medvedev has secured 21 championships at 21 various events.
"It's the first time I'm at a tournament with my two daughters simultaneously, so to secure a trophy is really nice," said world number 14 Daniil Medvedev.
"This title is in honour of my second daughter my daughter, because the first title I won when my older daughter my daughter was delivered was for her."
The tennis star, the past champion, had been defeated in his previous six championship matches, including in that event in the past months.
Medvedev's counter-punching strategy and recurring emotional displays on court had led observers to wonder if his ability to perform at the elite level was over.
Yet the 29-year-old has altered his approach in recent weeks, making an effort to come to the net and compete assertively, reinforced by an enhanced serve.
The champion came back from a break down in the opening set against the challenging opponent, securing four of the final five games to go ahead.
Both players traded break points in the following set before the Frenchman, striving for his maiden professional title, took control to create a final set.
The opponent rescued four early opportunities in a competitive third set before the champion broke to 15 to serve for the match.
Appropriately, Medvedev secured the title with a rally at the net area, with his opponent unable to control a shot after a lengthy match.