19 of the Russian's 21 titles have been achieved on hard courts
A resurgent the Russian player won his maiden trophy for over two years with victory over opponent Moutet in the tournament final.
Medvedev, a ex- world number one, has experienced a difficult year, managing just a single victory at the Grand Slams and suffering a difficult moment at the US Open.
His varied form on the tennis tour - and difficulties with his service game in particular - resulted in him exiting of the elite rankings and finally separating with long-term coach his previous coach.
Presently working with Johansson and his other coach, Medvedev has steadily advanced in the last few weeks - climaxing in a tightly fought three-set victory over challenger Moutet.
This marks Medvedev's maiden trophy following the Rome competition and first on a hardcourt from that period of that year.
Success also means he has achieved twenty-one victories at twenty-one various tournaments.
"For the first time I am participating in a competition with my two daughters together, so to win a trophy is especially meaningful," said world number 14 Medvedev.
"This championship is in honour of my second daughter her name, because the initial championship I achieved when my child my daughter was born was for her."
Medvedev, the former major winner, had been defeated in his past six title deciders, comprising in Halle earlier this year.
Medvedev's retrieving strategy and recurring reactions on the playing surface had prompted some to wonder if his skill to compete at the highest level was over.
However the player has made changes in recent weeks, making an effort to advance forward and compete aggressively, supported by an enhanced serving game.
He fought back from a deficit in the opening set against the difficult Frenchman, winning 4 of the concluding five games to take the lead.
The pair traded service breaks in the second set before the challenger, striving for his initial ATP Tour victory, seized the initiative to force a decider.
The opponent defended 4 early-game opportunities in a competitive final set before the Russian broke to fifteen to secure the win.
Appropriately, Medvedev clinched the title with a rally at the front of the court, with his opponent failing to manage a shot after a lengthy match.