Nineteen of Medvedev's 21 victories have been achieved on hard courts
A resurgent the Russian player secured his first championship for over two years with a win over opponent Moutet in the competition championship match.
Medvedev, a ex- world number one, has endured a challenging period, managing just one win at the big events and undergoing a meltdown at the US Open.
The player's inconsistency on the professional circuit - and issues with his serve in particular - resulted in him falling of the world's top 10 and finally separating with long-time trainer his previous coach.
Currently working with his coach and Goetzke, he has steadily progressed in the past month - peaking in a closely contested 7-5 4-6 6-3 win over opponent Corentin Moutet.
This represents his maiden championship following the Italian tournament and maiden on a hard court from March of the previous year.
Victory also indicates he has won twenty-one victories at 21 various competitions.
"For the first time I have attended a competition with my two daughters simultaneously, so to win a trophy is particularly special," commented world number 14 the champion.
"This victory is in tribute of my child my daughter, because the first title I achieved when my child her name was delivered was for her."
The athlete, the past champion, had been defeated in his last six championship matches, comprising in that event previously this season.
The player's counter-punching strategy and frequent reactions on the tennis court had prompted some to wonder if his capacity to play at the top level was concluded.
Yet the player has altered his approach in the past month, making an effort to advance forward and perform aggressively, backed up by an improved serve.
The champion recovered from a deficit in the opening set against the tricky opponent, taking 4 of the concluding five exchanges to go ahead.
Both players exchanged breaks in the following set before the challenger, striving for his first professional title, seized the initiative to create a decider.
The opponent defended four initial break points in a competitive deciding set before the Russian broke to that score to close out the victory.
Fittingly, Medvedev clinched victory with a point at the front of the court, with the Frenchman incapable to control a shot after a lengthy match.