19 of the Russian's twenty-one titles have been won on hard surfaces
A comeback the Russian player claimed his first title for nearly 30 months with victory over opponent Moutet in the competition championship match.
The Russian, a ex- top-ranked player, has had a torrid period, achieving just one win at the Grand Slams and experiencing a meltdown at the New York tournament.
The player's varied form on the tennis tour - and issues with his serve in particular - caused him falling of the world's top 10 and eventually separating with long-time trainer his previous coach.
Presently training with his coach and his other coach, he has steadily progressed in the past month - climaxing in a hard-fought three-set victory over Frenchman Moutet.
It is the player's first trophy after the Italian tournament and first on a hard surface from March of 2023.
The win also signifies he has won 21 championships at 21 various competitions.
"It's the first time I have attended a event with my children together, so to secure a championship is particularly special," said world number 14 Medvedev.
"This title is in honour of my child my daughter, because the initial championship I achieved when my older daughter Alisa was born was for her."
Medvedev, the former major winner, had been defeated in his last six championship matches, including in that event in the past months.
The player's counter-punching approach and recurring outbursts on court had caused observers to doubt if his ability to compete at the highest level was finished.
But the player has altered his approach in the last few weeks, striving to approach the net and compete aggressively, supported by an better serve.
The champion fought back from a break down in the opening set against the difficult opponent, winning 4 of the last five games to gain the advantage.
The pair exchanged breaks in the following set before the Frenchman, attempting for his maiden ATP Tour victory, gained dominance to force a final set.
Moutet saved 4 initial chances in a tight final set before Medvedev secured a break to 15 to serve for the match.
Appropriately, the winner secured victory with a point at the front of the court, with Moutet failing to control a return after over two and a half hours.
