19 of Medvedev's twenty-one championships have been won on hard courts
A resurgent the Russian player secured his first trophy for over two years with victory over opponent Moutet in the competition final.
The athlete, a ex- world number one, has experienced a difficult season, winning just one win at the Grand Slams and experiencing a meltdown at the New York tournament.
His unpredictability on the tennis tour - and issues with his service game in especial - caused him dropping out of the elite rankings and eventually separating with former coach Gilles Cervara.
Currently training with his coach and his other coach, he has consistently progressed in the past month - climaxing in a tightly fought three-set victory over challenger Moutet.
This represents the player's first trophy following the Italian tournament and initial on a hardcourt from March of that year.
Success also means the Russian has achieved 21 championships at twenty-one different events.
"This marks the first occasion I'm at a event with my both daughters simultaneously, so to get a title is especially meaningful," said world number 14 the champion.
"This championship is in dedication of my second daughter her name, because the first title I achieved when my older daughter my daughter was delivered was for her."
Medvedev, the former major winner, had been defeated in his previous six championship matches, including in that event in the past months.
His defensive play style and frequent outbursts on the tennis court had caused observers to question if his ability to compete at the elite level was over.
But the athlete has implemented adjustments in recent weeks, making an effort to come to the net and perform aggressively, backed up by an improved service.
The champion recovered from a disadvantage in the initial set against the difficult Frenchman, taking 4 of the final five games to take the lead.
The pair exchanged break points in the middle set before the challenger, bidding for his initial ATP Tour title, seized the initiative to push for a final set.
The opponent defended 4 initial opportunities in a close third set before the champion secured a break to fifteen to serve for the match.
Fittingly, he earned victory with a rally at the net, with Moutet incapable to handle a return after over two and a half hours.