Nineteen of Medvedev's twenty-one championships have been earned on hard courts
A comeback Medvedev won his initial championship for nearly 30 months with success over opponent Moutet in the tournament title decider.
Medvedev, a former world number one, has had a difficult year, managing just one match at the big events and experiencing a meltdown at the US Open.
The player's unpredictability on the ATP Tour - and difficulties with his serving in particular - led to him falling of the top ten and finally splitting with long-term coach his previous coach.
Presently working with his coach and Rohan Goetzke, Medvedev has consistently progressed in the recent weeks - culminating in a hard-fought three-set win over opponent Moutet.
This represents Medvedev's first championship following the Italian tournament and maiden on a hard surface from March of that year.
Victory also indicates the Russian has won twenty-one championships at twenty-one different competitions.
"For the first time I'm at a tournament with my both daughters at once, so to win a championship is really nice," said tennis professional Medvedev.
"This title is in dedication of my second daughter her name, because the first title I got when my older daughter my daughter was born was for her."
The tennis star, the 2021 US Open champion, had failed in his past six championship matches, featuring in Halle previously this season.
The player's retrieving strategy and recurring outbursts on the playing surface had caused observers to doubt if his skill to perform at the top level was finished.
Yet the athlete has implemented adjustments in the last few weeks, making an effort to advance forward and compete positively, supported by an enhanced serve.
He came back from a break down in the first set against the challenging Frenchman, securing four of the concluding five games to go ahead.
The pair exchanged breaks in the middle set before the challenger, striving for his first ATP Tour championship, gained dominance to force a final set.
The opponent saved 4 early break points in a competitive final set before Medvedev secured a break to that score to serve for the match.
Suitably, he earned the title with a shot at the front of the court, with Moutet failing to manage a volley after over two and a half hours.