Nineteen of the Russian's 21 victories have been won on hard courts
A resurgent Medvedev won his maiden championship for over two years with victory over opponent Moutet in the Almaty Open title decider.
The athlete, a former world number one, has experienced a challenging period, managing just one match at the big events and experiencing a meltdown at the US Open.
Medvedev's unpredictability on the ATP Tour - and difficulties with his service game in specific - resulted in him falling of the elite rankings and finally splitting with long-time trainer Cervara.
Currently training with Thomas Johansson and Rohan Goetzke, he has gradually improved in the last few weeks - peaking in a closely contested three-set win over Frenchman Moutet.
It is the player's maiden championship since the 2023 Rome Masters and first on a hard court after spring of that year.
Victory also means Medvedev has won 21 victories at 21 distinct events.
"This marks the first occasion I have attended a competition with my children at once, so to win a title is especially meaningful," commented tennis professional Daniil Medvedev.
"This title is in honour of my younger daughter her name, because the first title I achieved when my older daughter my daughter was born was for her."
Medvedev, the former major winner, had failed in his previous six finals, comprising in the German tournament previously this season.
Medvedev's defensive approach and regular reactions on the playing surface had led commentators to doubt if his capacity to compete at the elite level was over.
Yet the 29-year-old has made changes in the last few weeks, making an effort to advance forward and compete aggressively, supported by an better service.
He came back from a deficit in the first set against the tricky opponent, taking four of the last five exchanges to gain the advantage.
The competitors swapped breaks in the middle set before the Frenchman, attempting for his initial tour victory, gained dominance to create a decider.
The opponent defended four initial opportunities in a tight final set before the champion secured a break to 15 to serve for the match.
Suitably, he secured the title with a point at the net, with his opponent unable to manage a volley after a lengthy match.
