Nineteen of Medvedev's twenty-one championships have been achieved on hard surfaces
A comeback Medvedev won his initial trophy for over two years with a win over opponent Moutet in the competition championship match.
The Russian, a former number one, has endured a challenging season, managing just one match at the major tournaments and suffering a meltdown at the American major.
Medvedev's unpredictability on the tennis tour - and issues with his serving in especial - caused him dropping out of the world's top 10 and eventually splitting with long-time mentor his previous coach.
Currently training with his coach and Rohan Goetzke, he has gradually improved in the recent weeks - culminating in a closely contested three-set triumph over opponent Moutet.
It is Medvedev's initial title since the 2023 Rome Masters and maiden on a hard surface since that period of the previous year.
Victory also signifies he has won twenty-one titles at 21 different competitions.
"For the first time I am participating in a tournament with my two daughters at once, so to win a trophy is really nice," stated world number 14 Daniil Medvedev.
"This championship is in tribute of my second daughter her name, because the initial championship I achieved when my older daughter her name was delivered was for her."
Medvedev, the past champion, had lost his last six championship matches, including in Halle in the past months.
His counter-punching approach and recurring outbursts on the playing surface had led commentators to doubt if his skill to play at the highest level was concluded.
Yet the athlete has implemented adjustments in the last few weeks, attempting to come to the net and play assertively, backed up by an improved serving game.
Medvedev recovered from a break down in the initial set against the tricky opponent, taking 4 of the final five games to gain the advantage.
The pair exchanged break points in the second set before the Frenchman, attempting for his initial tour championship, gained dominance to push for a decider.
He rescued 4 early-game chances in a tight deciding set before the Russian secured a break to that score to close out the victory.
Fittingly, the winner earned the title with a shot at the net area, with the Frenchman failing to manage a volley after two hours and 38 minutes.