Nineteen of Medvedev's 21 championships have been achieved on hard surfaces
A comeback Medvedev secured his initial title for over two years with a win over opponent Moutet in the competition final.
The Russian, a former top-ranked player, has had a challenging season, achieving just one win at the big events and suffering a difficult moment at the American major.
His inconsistency on the professional circuit - and issues with his serving in specific - resulted in him exiting of the world's top 10 and finally parting ways with long-term trainer his previous coach.
Now training with his coach and Goetzke, he has steadily advanced in the last few weeks - climaxing in a closely contested three-set triumph over opponent Corentin Moutet.
It is Medvedev's initial championship following the Rome competition and initial on a hard surface after spring of that year.
Success also means the Russian has achieved twenty-one championships at 21 different tournaments.
"For the first time I am participating in a competition with my two daughters together, so to win a championship is particularly special," said tennis professional the champion.
"This title is in dedication of my younger daughter Victoria, because the first title I won when my older daughter Alisa was delivered was for her."
The tennis star, the past champion, had lost his past six championship matches, including in that event earlier this year.
Medvedev's counter-punching strategy and frequent emotional displays on the playing surface had caused some to question if his ability to play at the elite level was finished.
Yet the 29-year-old has altered his approach in the last few weeks, making an effort to come to the net and play positively, reinforced by an improved serving game.
The champion fought back from a deficit in the first set against the challenging Frenchman, taking four of the concluding five exchanges to go ahead.
The competitors swapped service breaks in the following set before Moutet, bidding for his first tour championship, took control to push for a third set.
Moutet saved 4 initial opportunities in a close deciding set before the champion secured a break to 15 to secure the win.
Suitably, the winner earned victory with a point at the front of the court, with Moutet incapable to manage a volley after over two and a half hours.
