Nineteen of the Russian's 21 victories have been earned on hard courts
A comeback Medvedev secured his maiden trophy for 882 days with success over opponent Moutet in the tournament final.
Medvedev, a ex- number one, has experienced a torrid period, achieving just a single victory at the major tournaments and suffering a meltdown at the US Open.
Medvedev's unpredictability on the ATP Tour - and difficulties with his serve in particular - led to him falling of the elite rankings and ultimately splitting with former coach Gilles Cervara.
Presently working with Thomas Johansson and Goetzke, Medvedev has steadily progressed in the past month - culminating in a closely contested competitive victory over opponent Moutet.
It is Medvedev's initial trophy after the 2023 Rome Masters and first on a hard court since spring of that year.
Victory also means Medvedev has achieved 21 victories at 21 distinct tournaments.
"It's the first time I'm at a competition with my both daughters together, so to win a trophy is particularly special," said ranked player Daniil Medvedev.
"This title is in tribute of my second daughter my daughter, because the initial championship I achieved when my child Alisa was born was for her."
The athlete, the past champion, had failed in his last six finals, comprising in the German tournament earlier this year.
The player's counter-punching approach and frequent outbursts on the playing surface had prompted observers to wonder if his skill to play at the elite level was finished.
However the player has altered his approach in the past month, attempting to approach the net and compete positively, backed up by an better serving game.
Medvedev came back from a break down in the opening set against the difficult opponent, securing four of the final five points to gain the advantage.
Both players swapped service breaks in the middle set before the challenger, striving for his maiden ATP Tour championship, took control to force a final set.
Moutet saved 4 early break points in a competitive third set before the Russian secured a break to that score to secure the win.
Suitably, he earned the win with a point at the net area, with the Frenchman unable to manage a return after over two and a half hours.
