Nineteen of the Russian's 21 championships have been earned on hard courts
A revitalized Medvedev secured his first trophy for 882 days with victory over opponent Moutet in the tournament title decider.
The athlete, a former world number one, has endured a difficult year, achieving just one match at the Grand Slams and suffering a setback at the American major.
The player's unpredictability on the ATP Tour - and struggles with his serving in specific - led to him exiting of the top ten and eventually splitting with long-time coach Cervara.
Presently working with Thomas Johansson and Rohan Goetzke, Medvedev has consistently progressed in the past month - peaking in a hard-fought 7-5 4-6 6-3 triumph over Frenchman Moutet.
It is Medvedev's first title after the Rome competition and initial on a hard surface from that period of that year.
Success also means Medvedev has won 21 titles at 21 various competitions.
"This marks the first occasion I'm at a tournament with my children at once, so to get a trophy is especially meaningful," said ranked player the champion.
"This title is in tribute of my younger daughter Victoria, because the initial championship I achieved when my child her name was born was for her."
The tennis star, the 2021 US Open champion, had lost his previous six title deciders, featuring in that event previously this season.
His counter-punching play style and frequent reactions on court had led some to question if his skill to compete at the highest level was over.
However the 29-year-old has made changes in recent weeks, making an effort to come to the net and play aggressively, supported by an better service.
He recovered from a break down in the opening set against the tricky Frenchman, securing 4 of the concluding five games to go ahead.
The competitors exchanged service breaks in the following set before Moutet, striving for his initial ATP Tour title, gained dominance to force a decider.
Moutet saved four early chances in a tight final set before Medvedev won the break to that score to serve for the match.
Fittingly, the winner earned the title with a shot at the net area, with Moutet failing to manage a shot after two hours and 38 minutes.
