Nineteen of Medvedev's twenty-one championships have been achieved on hard courts
A comeback the Russian player won his maiden title for 882 days with success over opponent Moutet in the competition championship match.
The athlete, a ex- world number one, has experienced a challenging season, achieving just a single victory at the big events and suffering a setback at the US Open.
His inconsistency on the tennis tour - and struggles with his service game in especial - caused him falling of the top ten and eventually parting ways with long-time coach Cervara.
Presently collaborating with Johansson and Rohan Goetzke, Medvedev has consistently improved in the last few weeks - climaxing in a hard-fought three-set victory over Frenchman Moutet.
It is the player's maiden championship after the Italian tournament and first on a hard surface after spring of 2023.
Success also indicates the Russian has won twenty-one victories at 21 different events.
"It's the first time I have attended a competition with my both daughters at once, so to secure a title is really nice," said ranked player Medvedev.
"This championship is in honour of my child Victoria, because the maiden victory I won when my first daughter my daughter was born was for her."
The tennis star, the past champion, had failed in his previous six championship matches, including in the German tournament earlier this year.
His retrieving approach and recurring reactions on court had led commentators to question if his skill to perform at the elite level was over.
Yet the player has made changes in recent weeks, attempting to come to the net and play aggressively, reinforced by an improved service.
He fought back from a break down in the initial set against the difficult Moutet, taking 4 of the concluding five exchanges to gain the advantage.
Both players exchanged breaks in the following set before the Frenchman, striving for his first professional title, seized the initiative to push for a third set.
The opponent saved 4 early-game chances in a close deciding set before the champion secured a break to that score to secure the win.
Appropriately, he secured the win with a point at the net, with Moutet unable to manage a return after two hours and 38 minutes.