Nineteen of the Russian's twenty-one championships have been achieved on hardcourt
A resurgent the Russian player secured his initial trophy for nearly 30 months with success over opponent Moutet in the Almaty Open championship match.
Medvedev, a ex- world number one, has experienced a challenging season, winning just a single victory at the major tournaments and undergoing a meltdown at the US Open.
The player's unpredictability on the tennis tour - and issues with his serving in especial - led to him falling of the elite rankings and finally parting ways with long-term mentor Gilles Cervara.
Now training with Thomas Johansson and his other coach, Medvedev has steadily progressed in the last few weeks - peaking in a tightly fought three-set win over opponent Moutet.
It is Medvedev's initial trophy since the Italian tournament and maiden on a hardcourt since that period of the previous year.
Victory also means the Russian has won twenty-one titles at 21 distinct competitions.
"It's the first time I am participating in a tournament with my children simultaneously, so to secure a championship is especially meaningful," commented ranked player the champion.
"This championship is in honour of my second daughter her name, because the initial championship I got when my child Alisa was born was for her."
Medvedev, the past champion, had lost his past six championship matches, featuring in that event previously this season.
The player's retrieving approach and regular outbursts on court had led commentators to wonder if his skill to play at the highest level was over.
However the player has altered his approach in the past month, attempting to approach the net and play aggressively, reinforced by an better service.
Medvedev fought back from a break down in the initial set against the difficult Frenchman, securing four of the final five points to gain the advantage.
The competitors swapped breaks in the following set before the Frenchman, striving for his maiden ATP Tour championship, seized the initiative to create a decider.
Moutet saved four early opportunities in a close final set before the Russian broke to that score to secure the win.
Fittingly, he secured victory with a point at the net area, with his opponent incapable to handle a volley after two hours and 38 minutes.
