Nineteen of Medvedev's 21 victories have been achieved on hard surfaces
A revitalized the Russian player claimed his first title for 882 days with success over opponent Moutet in the competition final.
The athlete, a former top-ranked player, has had a challenging season, winning just one win at the major tournaments and undergoing a meltdown at the US Open.
Medvedev's inconsistency on the tennis tour - and difficulties with his serving in specific - resulted in him falling of the world's top 10 and finally parting ways with former trainer Cervara.
Currently training with his coach and Rohan Goetzke, he has steadily progressed in the recent weeks - peaking in a hard-fought three-set win over challenger Moutet.
It is the player's first trophy following the Rome competition and initial on a hard surface from spring of the previous year.
The win also means the Russian has achieved 21 titles at 21 distinct events.
"For the first time I am participating in a competition with my children together, so to get a title is really nice," said tennis professional the champion.
"This victory is in dedication of my second daughter her name, because the first title I achieved when my child my daughter was delivered was for her."
The tennis star, the former major winner, had been defeated in his past six finals, including in that event previously this season.
Medvedev's defensive play style and regular reactions on the tennis court had led some to doubt if his capacity to compete at the top level was finished.
However the player has made changes in the past month, striving to approach the net and perform positively, reinforced by an better service.
Medvedev fought back from a disadvantage in the initial set against the challenging Frenchman, taking four of the final five games to go ahead.
The competitors exchanged breaks in the following set before the challenger, striving for his first ATP Tour victory, took control to force a third set.
Moutet rescued 4 early chances in a close deciding set before the Russian won the break to that score to secure the win.
Fittingly, the winner earned the win with a point at the front of the court, with the Frenchman unable to control a volley after two hours and 38 minutes.
