Nineteen of the Russian's 21 championships have been achieved on hard surfaces
A resurgent the Russian player won his maiden title for 882 days with victory over opponent Moutet in the competition final.
The athlete, a former world number one, has had a challenging period, managing just a single victory at the major tournaments and experiencing a difficult moment at the US Open.
The player's inconsistency on the professional circuit - and struggles with his serving in particular - caused him exiting of the world's top 10 and eventually separating with former coach Gilles Cervara.
Presently collaborating with his coach and Rohan Goetzke, he has gradually advanced in the recent weeks - culminating in a tightly fought three-set victory over challenger Corentin Moutet.
This represents the player's first title since the Rome competition and first on a hard court since that period of that year.
Success also indicates he has achieved twenty-one championships at 21 different competitions.
"This marks the first occasion I have attended a tournament with my both daughters simultaneously, so to secure a championship is particularly special," commented world number 14 the champion.
"This championship is in dedication of my child my daughter, because the first title I got when my child her name was born was for her."
The tennis star, the former major winner, had failed in his past six title deciders, including in that event earlier this year.
Medvedev's retrieving approach and recurring outbursts on court had prompted observers to doubt if his ability to play at the highest level was finished.
But the 29-year-old has made changes in the past month, attempting to advance forward and compete positively, reinforced by an enhanced serve.
Medvedev recovered from a deficit in the opening set against the tricky Frenchman, winning four of the last five exchanges to go ahead.
The competitors traded breaks in the second set before the challenger, bidding for his initial ATP Tour title, seized the initiative to force a decider.
Moutet rescued four initial opportunities in a tight third set before the Russian won the break to 15 to secure the win.
Appropriately, Medvedev clinched the win with a rally at the front of the court, with Moutet failing to manage a return after two hours and 38 minutes.
