Nineteen of Medvedev's 21 titles have been earned on hard surfaces
A revitalized the Russian player won his first championship for 882 days with a win over opponent Moutet in the Almaty Open championship match.
The athlete, a former world number one, has had a torrid year, achieving just one win at the major tournaments and suffering a setback at the New York tournament.
Medvedev's unpredictability on the professional circuit - and struggles with his serving in specific - resulted in him dropping out of the top ten and ultimately parting ways with long-term trainer his previous coach.
Currently training with his coach and Rohan Goetzke, Medvedev has steadily progressed in the last few weeks - climaxing in a closely contested competitive triumph over Frenchman Moutet.
This represents the player's initial championship following the 2023 Rome Masters and initial on a hard court since that period of the previous year.
The win also signifies Medvedev has achieved 21 titles at twenty-one various events.
"For the first time I'm at a tournament with my two daughters simultaneously, so to get a title is especially meaningful," stated world number 14 Medvedev.
"This title is in dedication of my child Victoria, because the initial championship I achieved when my child Alisa was born was for her."
The tennis star, the former major winner, had failed in his past six finals, including in that event earlier this year.
Medvedev's retrieving play style and regular emotional displays on court had caused some to question if his skill to compete at the highest level was finished.
Yet the player has made changes in the last few weeks, attempting to come to the net and perform aggressively, backed up by an better serve.
He came back from a deficit in the initial set against the difficult opponent, winning four of the final five games to take the lead.
Both players traded breaks in the second set before the challenger, striving for his initial ATP Tour title, gained dominance to create a third set.
The opponent rescued 4 early chances in a tight final set before Medvedev broke to fifteen to close out the victory.
Fittingly, Medvedev secured the title with a shot at the front of the court, with the Frenchman failing to control a return after over two and a half hours.