19 of the Russian's 21 championships have been earned on hardcourt
A revitalized the Russian player claimed his initial trophy for 882 days with victory over opponent Moutet in the competition championship match.
Medvedev, a former world number one, has endured a challenging year, winning just one win at the Grand Slams and undergoing a setback at the US Open.
Medvedev's unpredictability on the professional circuit - and difficulties with his serve in specific - caused him falling of the top ten and eventually splitting with long-time mentor his previous coach.
Now working with Thomas Johansson and his other coach, Medvedev has steadily progressed in the past month - culminating in a hard-fought three-set triumph over Frenchman Moutet.
This marks his initial championship since the Rome competition and initial on a hard surface from that period of that year.
Success also means he has achieved twenty-one victories at twenty-one distinct tournaments.
"It's the first time I am participating in a event with my both daughters simultaneously, so to win a trophy is particularly special," said world number 14 the champion.
"This title is in honour of my child my daughter, because the maiden victory I won when my child Alisa was delivered was for her."
Medvedev, the 2021 US Open champion, had lost his previous six title deciders, including in the German tournament earlier this year.
His counter-punching play style and recurring reactions on court had prompted observers to question if his ability to play at the top level was finished.
But the player has altered his approach in recent weeks, making an effort to approach the net and perform assertively, backed up by an improved service.
Medvedev came back from a break down in the first set against the difficult opponent, winning four of the concluding five games to gain the advantage.
Both players traded break points in the middle set before Moutet, bidding for his maiden ATP Tour victory, took control to create a third set.
Moutet saved 4 early opportunities in a tight third set before the champion won the break to that score to secure the win.
Suitably, he secured the title with a rally at the net, with Moutet incapable to handle a return after a lengthy match.