Nineteen of the Russian's 21 victories have been earned on hardcourt
A comeback the Russian player secured his initial title for over two years with success over opponent Moutet in the competition championship match.
The athlete, a former world number one, has had a difficult period, winning just one win at the Grand Slams and experiencing a meltdown at the New York tournament.
His unpredictability on the professional circuit - and difficulties with his serving in specific - caused him falling of the top ten and finally separating with long-term trainer Cervara.
Presently collaborating with his coach and his other coach, he has steadily improved in the past month - peaking in a hard-fought 7-5 4-6 6-3 triumph over opponent Moutet.
This marks his initial trophy since the Italian tournament and maiden on a hard surface after that period of that year.
Success also means Medvedev has won twenty-one championships at twenty-one different tournaments.
"For the first time I am participating in a event with my children together, so to win a title is particularly special," said world number 14 the champion.
"This championship is in honour of my younger daughter my daughter, because the initial championship I achieved when my child her name was born was for her."
Medvedev, the past champion, had lost his last six championship matches, featuring in the German tournament previously this season.
Medvedev's defensive strategy and regular outbursts on the playing surface had prompted commentators to question if his ability to perform at the elite level was finished.
However the 29-year-old has implemented adjustments in the last few weeks, striving to advance forward and perform positively, backed up by an better service.
Medvedev came back from a disadvantage in the opening set against the difficult Moutet, securing 4 of the final five games to go ahead.
The competitors exchanged breaks in the following set before the Frenchman, bidding for his maiden professional title, seized the initiative to push for a third set.
The opponent saved four early chances in a competitive third set before Medvedev secured a break to fifteen to close out the victory.
Suitably, he secured the title with a shot at the net area, with the Frenchman unable to manage a return after two hours and 38 minutes.