Nineteen of the Russian's 21 championships have been achieved on hard courts
A comeback Medvedev secured his initial title for 882 days with a win over opponent Moutet in the competition championship match.
Medvedev, a ex- top-ranked player, has had a challenging season, winning just one win at the major tournaments and experiencing a setback at the US Open.
His unpredictability on the ATP Tour - and issues with his service game in especial - caused him exiting of the top ten and finally parting ways with long-term trainer Gilles Cervara.
Currently collaborating with Thomas Johansson and his other coach, Medvedev has steadily improved in the last few weeks - peaking in a tightly fought three-set triumph over Frenchman Moutet.
It is his first title after the 2023 Rome Masters and maiden on a hard surface after that period of that year.
Victory also means the Russian has secured 21 titles at 21 various competitions.
"It's the first time I have attended a competition with my children simultaneously, so to secure a trophy is particularly special," commented ranked player the champion.
"This title is in tribute of my second daughter Victoria, because the initial championship I won when my first daughter my daughter was born was for her."
The tennis star, the former major winner, had lost his past six championship matches, including in that event previously this season.
The player's defensive strategy and recurring outbursts on the playing surface had led commentators to doubt if his ability to compete at the top level was finished.
Yet the athlete has made changes in the past month, striving to advance forward and perform assertively, backed up by an better service.
Medvedev came back from a deficit in the opening set against the difficult opponent, winning four of the final five games to go ahead.
The pair traded break points in the following set before Moutet, attempting for his first professional championship, seized the initiative to force a decider.
Moutet rescued four early-game break points in a competitive deciding set before the Russian won the break to fifteen to serve for the match.
Suitably, the winner earned the win with a rally at the front of the court, with the Frenchman failing to manage a shot after over two and a half hours.
