19 of the Russian's twenty-one titles have been earned on hard courts
A comeback Medvedev won his first title for over two years with victory over opponent Moutet in the tournament championship match.
Medvedev, a former world number one, has experienced a challenging period, managing just a single victory at the big events and suffering a difficult moment at the US Open.
Medvedev's unpredictability on the professional circuit - and struggles with his serving in particular - resulted in him falling of the world's top 10 and ultimately separating with long-time mentor his previous coach.
Now working with Thomas Johansson and Goetzke, Medvedev has steadily advanced in the past month - climaxing in a tightly fought three-set win over challenger Moutet.
This represents his maiden trophy after the Italian tournament and maiden on a hard surface since that period of that year.
Victory also signifies the Russian has won 21 victories at 21 distinct tournaments.
"It's the first time I'm at a competition with my two daughters simultaneously, so to win a trophy is particularly special," stated ranked player the champion.
"This victory is in dedication of my younger daughter my daughter, because the maiden victory I won when my child Alisa was born was for her."
The tennis star, the former major winner, had lost his last six finals, comprising in Halle earlier this year.
Medvedev's counter-punching approach and regular reactions on the playing surface had led observers to doubt if his skill to compete at the highest level was over.
Yet the athlete has implemented adjustments in the last few weeks, attempting to approach the net and play positively, supported by an improved service.
Medvedev fought back from a deficit in the first set against the tricky opponent, taking 4 of the last five points to take the lead.
The pair swapped breaks in the following set before the challenger, attempting for his initial ATP Tour victory, gained dominance to push for a decider.
He defended four early chances in a close final set before the Russian won the break to that score to close out the victory.
Appropriately, Medvedev clinched the win with a shot at the net, with the Frenchman incapable to manage a volley after over two and a half hours.