Nineteen of the Russian's 21 championships have been earned on hard surfaces
A resurgent the Russian player claimed his initial championship for 882 days with success over opponent Moutet in the tournament final.
The athlete, a ex- number one, has experienced a difficult season, managing just one match at the big events and experiencing a setback at the New York tournament.
His unpredictability on the professional circuit - and issues with his service game in specific - led to him falling of the world's top 10 and eventually parting ways with long-term mentor his previous coach.
Now working with Thomas Johansson and Goetzke, Medvedev has steadily progressed in the past month - peaking in a hard-fought three-set triumph over opponent Moutet.
This represents the player's maiden championship following the Rome competition and first on a hard surface since spring of 2023.
The win also means the Russian has achieved twenty-one victories at 21 distinct competitions.
"This marks the first occasion I am participating in a event with my two daughters simultaneously, so to win a championship is really nice," said ranked player Medvedev.
"This championship is in tribute of my second daughter Victoria, because the first title I got when my child her name was delivered was for her."
The athlete, the 2021 US Open champion, had been defeated in his previous six finals, comprising in that event in the past months.
His counter-punching strategy and frequent reactions on court had prompted some to wonder if his ability to play at the top level was concluded.
Yet the 29-year-old has altered his approach in the past month, attempting to advance forward and play aggressively, reinforced by an better serving game.
Medvedev recovered from a break down in the initial set against the challenging Frenchman, taking 4 of the concluding five points to go ahead.
The competitors traded service breaks in the middle set before the Frenchman, attempting for his first ATP Tour victory, took control to force a final set.
He rescued four early-game opportunities in a competitive third set before the champion secured a break to 15 to serve for the match.
Fittingly, Medvedev secured the title with a rally at the net area, with his opponent incapable to handle a return after two hours and 38 minutes.