19 of Medvedev's twenty-one victories have been achieved on hard courts
A comeback the Russian player secured his maiden title for 882 days with victory over opponent Moutet in the tournament championship match.
The Russian, a ex- world number one, has endured a challenging season, managing just one match at the Grand Slams and experiencing a difficult moment at the New York tournament.
His unpredictability on the professional circuit - and difficulties with his serve in especial - caused him exiting of the top ten and finally splitting with long-term mentor Gilles Cervara.
Now training with his coach and his other coach, Medvedev has consistently progressed in the past month - culminating in a closely contested three-set triumph over opponent Corentin Moutet.
This represents his maiden title following the Rome competition and maiden on a hardcourt from March of that year.
Victory also indicates the Russian has achieved 21 victories at twenty-one distinct events.
"It's the first time I'm at a event with my both daughters together, so to win a trophy is really nice," said tennis professional Medvedev.
"This victory is in tribute of my younger daughter her name, because the initial championship I achieved when my older daughter her name was delivered was for her."
The tennis star, the past champion, had lost his past six title deciders, including in Halle earlier this year.
The player's counter-punching strategy and frequent emotional displays on the tennis court had caused some to question if his skill to perform at the elite level was concluded.
However the player has implemented adjustments in recent weeks, attempting to advance forward and perform assertively, backed up by an enhanced service.
He recovered from a break down in the first set against the difficult Frenchman, winning 4 of the final five points to go ahead.
Both players traded breaks in the following set before the challenger, attempting for his first ATP Tour victory, gained dominance to create a decider.
The opponent rescued four initial chances in a tight deciding set before Medvedev secured a break to that score to close out the victory.
Fittingly, he earned victory with a point at the net area, with Moutet unable to manage a shot after a lengthy match.