Nineteen of the Russian's 21 titles have been achieved on hardcourt
A comeback Medvedev secured his initial trophy for nearly 30 months with victory over opponent Moutet in the Almaty Open championship match.
The athlete, a ex- top-ranked player, has had a challenging year, achieving just a single victory at the Grand Slams and undergoing a setback at the American major.
Medvedev's inconsistency on the ATP Tour - and issues with his service game in specific - led to him falling of the top ten and finally splitting with long-term coach Gilles Cervara.
Presently collaborating with Thomas Johansson and Rohan Goetzke, he has gradually improved in the past month - climaxing in a closely contested 7-5 4-6 6-3 win over challenger Corentin Moutet.
It is his initial trophy after the Rome competition and maiden on a hard surface from that period of 2023.
Success also signifies he has achieved 21 championships at 21 various events.
"It's the first time I have attended a event with my two daughters simultaneously, so to secure a championship is really nice," stated world number 14 the champion.
"This title is in tribute of my second daughter her name, because the first title I achieved when my first daughter Alisa was born was for her."
Medvedev, the former major winner, had been defeated in his last six championship matches, including in Halle in the past months.
The player's counter-punching approach and recurring emotional displays on court had caused observers to wonder if his capacity to compete at the top level was finished.
Yet the athlete has altered his approach in recent weeks, striving to approach the net and play assertively, supported by an enhanced service.
He came back from a disadvantage in the opening set against the challenging Frenchman, securing 4 of the last five points to go ahead.
The pair swapped service breaks in the following set before the Frenchman, bidding for his initial tour victory, seized the initiative to force a decider.
The opponent saved 4 early-game break points in a tight deciding set before the champion won the break to that score to serve for the match.
Appropriately, Medvedev clinched the win with a point at the net area, with Moutet failing to control a volley after two hours and 38 minutes.