Nineteen of the Russian's 21 championships have been won on hard surfaces
A revitalized Medvedev claimed his first title for over two years with a win over opponent Moutet in the competition title decider.
The athlete, a former top-ranked player, has had a difficult season, managing just one win at the big events and undergoing a meltdown at the US Open.
Medvedev's inconsistency on the ATP Tour - and difficulties with his serving in particular - led to him falling of the world's top 10 and finally splitting with former trainer his previous coach.
Currently collaborating with Thomas Johansson and Goetzke, he has steadily improved in the past month - climaxing in a closely contested 7-5 4-6 6-3 triumph over challenger Moutet.
It is the player's first trophy since the 2023 Rome Masters and initial on a hard surface after March of 2023.
Success also indicates Medvedev has won 21 victories at 21 different competitions.
"It's the first time I have attended a event with my children simultaneously, so to get a trophy is especially meaningful," stated ranked player Daniil Medvedev.
"This championship is in honour of my younger daughter Victoria, because the initial championship I won when my first daughter Alisa was delivered was for her."
Medvedev, the 2021 US Open champion, had failed in his last six title deciders, including in that event previously this season.
Medvedev's retrieving strategy and regular reactions on the playing surface had caused commentators to question if his ability to perform at the top level was finished.
But the athlete has implemented adjustments in recent weeks, making an effort to come to the net and compete assertively, backed up by an enhanced service.
Medvedev fought back from a break down in the opening set against the challenging Moutet, winning 4 of the concluding five exchanges to take the lead.
Both players traded breaks in the following set before Moutet, bidding for his first professional victory, seized the initiative to push for a final set.
Moutet saved 4 early chances in a competitive third set before the champion won the break to 15 to serve for the match.
Fittingly, he secured victory with a shot at the net, with his opponent unable to manage a shot after a lengthy match.