19 of Medvedev's 21 titles have been won on hard surfaces
A comeback Medvedev claimed his initial championship for nearly 30 months with a win over opponent Moutet in the tournament championship match.
The athlete, a former world number one, has had a challenging period, managing just one win at the major tournaments and suffering a setback at the US Open.
His inconsistency on the tennis tour - and issues with his serving in particular - resulted in him dropping out of the elite rankings and eventually separating with long-time coach Gilles Cervara.
Currently training with Thomas Johansson and his other coach, the tennis star has consistently progressed in the recent weeks - climaxing in a tightly fought competitive triumph over challenger Corentin Moutet.
This marks Medvedev's maiden title since the Rome competition and initial on a hard surface after that period of that year.
Victory also signifies the Russian has secured 21 victories at twenty-one various competitions.
"This marks the first occasion I'm at a competition with my both daughters simultaneously, so to secure a championship is particularly special," commented tennis professional Medvedev.
"This championship is in dedication of my younger daughter my daughter, because the initial championship I won when my child my daughter was born was for her."
The tennis star, the past champion, had been defeated in his last six finals, including in the German tournament earlier this year.
His defensive play style and frequent outbursts on the tennis court had led some to question if his ability to play at the top level was over.
However the athlete has made changes in the last few weeks, attempting to advance forward and compete assertively, reinforced by an improved serve.
The champion recovered from a break down in the initial set against the tricky Frenchman, securing four of the last five games to gain the advantage.
The competitors swapped service breaks in the following set before the challenger, striving for his initial professional title, took control to create a third set.
He defended four early break points in a tight final set before the Russian broke to 15 to secure the win.
Suitably, he earned the win with a point at the net area, with the Frenchman unable to manage a volley after a lengthy match.