Nineteen of the Russian's 21 championships have been earned on hard courts
A comeback the Russian player secured his maiden championship for nearly 30 months with success over opponent Moutet in the tournament final.
Medvedev, a former world number one, has endured a torrid period, managing just one win at the major tournaments and suffering a difficult moment at the American major.
The player's varied form on the professional circuit - and issues with his service game in especial - caused him falling of the top ten and ultimately separating with long-time coach his previous coach.
Currently training with Thomas Johansson and his other coach, Medvedev has steadily advanced in the recent weeks - culminating in a closely contested three-set win over Frenchman Moutet.
This represents Medvedev's maiden championship after the 2023 Rome Masters and initial on a hard court from that period of that year.
Success also means he has won 21 championships at 21 different tournaments.
"This marks the first occasion I'm at a event with my children together, so to win a trophy is particularly special," stated world number 14 Medvedev.
"This championship is in tribute of my second daughter my daughter, because the first title I won when my child her name was born was for her."
The athlete, the 2021 US Open champion, had failed in his past six championship matches, comprising in Halle previously this season.
Medvedev's defensive play style and frequent reactions on the tennis court had led observers to doubt if his ability to perform at the highest level was over.
However the athlete has made changes in the last few weeks, making an effort to come to the net and compete positively, backed up by an improved service.
He recovered from a break down in the initial set against the challenging opponent, winning four of the concluding five exchanges to gain the advantage.
The pair exchanged breaks in the middle set before Moutet, attempting for his maiden professional championship, took control to create a third set.
Moutet saved four initial break points in a close third set before Medvedev secured a break to that score to close out the victory.
Suitably, Medvedev earned victory with a point at the net area, with the Frenchman incapable to handle a volley after a lengthy match.
