Nineteen of Medvedev's 21 championships have been won on hard surfaces
A revitalized the Russian player secured his first trophy for over two years with a win over opponent Moutet in the tournament championship match.
The athlete, a ex- top-ranked player, has experienced a challenging season, managing just one match at the big events and undergoing a difficult moment at the New York tournament.
Medvedev's inconsistency on the tennis tour - and difficulties with his service game in specific - resulted in him dropping out of the world's top 10 and eventually parting ways with long-term mentor his previous coach.
Now training with his coach and his other coach, the tennis star has gradually progressed in the past month - peaking in a hard-fought competitive win over opponent Corentin Moutet.
This marks the player's first championship since the Italian tournament and initial on a hard surface since spring of that year.
Success also signifies the Russian has achieved 21 titles at 21 various events.
"This marks the first occasion I have attended a event with my both daughters together, so to get a championship is really nice," commented ranked player Medvedev.
"This victory is in honour of my second daughter my daughter, because the maiden victory I achieved when my older daughter my daughter was delivered was for her."
Medvedev, the former major winner, had lost his previous six championship matches, including in the German tournament previously this season.
His retrieving play style and recurring outbursts on the playing surface had prompted observers to doubt if his skill to play at the elite level was over.
However the player has made changes in the past month, attempting to come to the net and perform assertively, backed up by an improved service.
The champion fought back from a break down in the first set against the tricky Moutet, securing four of the last five games to take the lead.
The pair traded break points in the middle set before the Frenchman, bidding for his first professional victory, gained dominance to create a decider.
The opponent saved four early chances in a close final set before Medvedev broke to 15 to secure the win.
Suitably, he clinched the title with a rally at the net area, with his opponent unable to control a shot after a lengthy match.