Nineteen of the Russian's twenty-one championships have been achieved on hard courts
A comeback the Russian player secured his first title for 882 days with success over opponent Moutet in the tournament final.
Medvedev, a former number one, has experienced a torrid period, managing just one win at the Grand Slams and suffering a setback at the US Open.
Medvedev's unpredictability on the professional circuit - and difficulties with his serve in specific - caused him dropping out of the world's top 10 and eventually separating with former trainer Cervara.
Presently working with Thomas Johansson and Goetzke, the tennis star has consistently improved in the past month - climaxing in a hard-fought three-set victory over opponent Moutet.
This represents Medvedev's maiden championship after the 2023 Rome Masters and initial on a hard court from that period of the previous year.
The win also means he has won 21 victories at twenty-one distinct tournaments.
"For the first time I have attended a competition with my both daughters at once, so to secure a trophy is especially meaningful," said ranked player Medvedev.
"This title is in dedication of my second daughter Victoria, because the first title I won when my child my daughter was delivered was for her."
Medvedev, the 2021 US Open champion, had failed in his past six finals, comprising in Halle previously this season.
His defensive strategy and recurring emotional displays on the tennis court had caused commentators to doubt if his ability to play at the top level was concluded.
However the player has altered his approach in the past month, attempting to advance forward and compete positively, supported by an enhanced service.
He recovered from a disadvantage in the first set against the challenging Frenchman, taking four of the last five games to gain the advantage.
The competitors swapped break points in the middle set before Moutet, attempting for his maiden tour title, took control to push for a third set.
Moutet rescued four early-game break points in a competitive final set before Medvedev broke to that score to secure the win.
Suitably, Medvedev earned the title with a shot at the front of the court, with the Frenchman incapable to manage a shot after two hours and 38 minutes.
