Nineteen of the Russian's twenty-one titles have been earned on hard surfaces
A resurgent the Russian player won his maiden title for 882 days with success over opponent Moutet in the competition championship match.
Medvedev, a ex- world number one, has had a challenging season, winning just one win at the big events and experiencing a difficult moment at the New York tournament.
Medvedev's inconsistency on the tennis tour - and struggles with his service game in specific - resulted in him dropping out of the elite rankings and finally separating with long-time coach his previous coach.
Currently collaborating with Johansson and Goetzke, he has gradually advanced in the past month - peaking in a tightly fought three-set win over opponent Corentin Moutet.
This marks Medvedev's first trophy since the Italian tournament and first on a hard surface from spring of the previous year.
Success also signifies he has secured 21 victories at twenty-one distinct competitions.
"This marks the first occasion I have attended a tournament with my children at once, so to secure a championship is really nice," commented world number 14 the champion.
"This title is in honour of my younger daughter my daughter, because the first title I won when my first daughter Alisa was born was for her."
The athlete, the former major winner, had been defeated in his past six title deciders, including in Halle earlier this year.
His counter-punching approach and frequent outbursts on court had led observers to wonder if his capacity to play at the elite level was over.
But the player has made changes in the past month, making an effort to advance forward and play positively, supported by an improved serve.
The champion fought back from a deficit in the initial set against the tricky opponent, securing 4 of the final five exchanges to take the lead.
Both players exchanged breaks in the following set before the Frenchman, bidding for his maiden professional championship, took control to create a decider.
He defended four early chances in a competitive final set before the Russian won the break to 15 to close out the victory.
Suitably, the winner clinched victory with a point at the net, with his opponent incapable to manage a volley after over two and a half hours.
