19 of the Russian's 21 titles have been won on hard courts
A comeback the Russian player claimed his initial championship for nearly 30 months with success over opponent Moutet in the tournament title decider.
The Russian, a ex- number one, has had a difficult year, managing just one win at the big events and suffering a difficult moment at the American major.
His unpredictability on the ATP Tour - and difficulties with his serving in specific - led to him exiting of the world's top 10 and ultimately parting ways with former trainer his previous coach.
Currently training with his coach and Rohan Goetzke, he has steadily progressed in the past month - climaxing in a closely contested three-set win over challenger Moutet.
It is the player's initial title since the Rome competition and initial on a hard surface after that period of the previous year.
Success also signifies the Russian has won twenty-one titles at twenty-one different events.
"It's the first time I have attended a tournament with my two daughters at once, so to win a trophy is really nice," said world number 14 Medvedev.
"This victory is in honour of my child Victoria, because the first title I won when my child her name was delivered was for her."
The tennis star, the 2021 US Open champion, had been defeated in his past six championship matches, featuring in Halle earlier this year.
The player's counter-punching approach and frequent emotional displays on the tennis court had prompted some to wonder if his skill to compete at the highest level was over.
But the player has altered his approach in the past month, striving to advance forward and compete positively, reinforced by an improved serve.
He came back from a disadvantage in the opening set against the tricky Frenchman, securing four of the concluding five exchanges to gain the advantage.
The pair exchanged break points in the middle set before the Frenchman, bidding for his maiden ATP Tour victory, seized the initiative to push for a decider.
Moutet defended 4 early opportunities in a close deciding set before the Russian won the break to that score to serve for the match.
Fittingly, he earned the win with a rally at the front of the court, with the Frenchman failing to handle a shot after over two and a half hours.
