Nineteen of Medvedev's twenty-one championships have been won on hardcourt
A resurgent the Russian player claimed his maiden title for over two years with victory over opponent Moutet in the competition final.
The athlete, a former world number one, has had a challenging period, managing just one match at the major tournaments and experiencing a difficult moment at the New York tournament.
His varied form on the tennis tour - and issues with his serve in especial - led to him dropping out of the elite rankings and eventually parting ways with long-time mentor his previous coach.
Now working with Johansson and Goetzke, Medvedev has gradually improved in the past month - culminating in a hard-fought 7-5 4-6 6-3 victory over opponent Moutet.
This marks the player's first trophy since the 2023 Rome Masters and maiden on a hard court after March of that year.
Success also indicates he has secured twenty-one championships at 21 different competitions.
"For the first time I am participating in a competition with my children at once, so to get a title is really nice," said tennis professional the champion.
"This championship is in dedication of my younger daughter her name, because the initial championship I achieved when my older daughter my daughter was born was for her."
Medvedev, the 2021 US Open champion, had failed in his last six championship matches, featuring in Halle in the past months.
His defensive strategy and frequent emotional displays on the playing surface had led observers to wonder if his ability to play at the elite level was finished.
Yet the 29-year-old has implemented adjustments in the past month, striving to come to the net and perform positively, supported by an enhanced serving game.
Medvedev recovered from a disadvantage in the first set against the difficult Moutet, securing 4 of the last five games to go ahead.
The pair traded break points in the middle set before Moutet, bidding for his maiden professional title, gained dominance to push for a third set.
Moutet saved 4 early-game chances in a close final set before the champion won the break to 15 to serve for the match.
Appropriately, Medvedev clinched the win with a shot at the net, with the Frenchman incapable to control a shot after two hours and 38 minutes.