Nineteen of the Russian's 21 titles have been earned on hard courts
A resurgent Medvedev won his first title for nearly 30 months with victory over opponent Moutet in the Almaty Open championship match.
Medvedev, a ex- world number one, has had a difficult season, achieving just one win at the Grand Slams and experiencing a meltdown at the American major.
Medvedev's varied form on the ATP Tour - and struggles with his serving in especial - caused him dropping out of the world's top 10 and eventually parting ways with former mentor Cervara.
Currently training with Thomas Johansson and Rohan Goetzke, Medvedev has gradually improved in the last few weeks - peaking in a closely contested competitive victory over opponent Moutet.
This represents his first trophy since the 2023 Rome Masters and maiden on a hard surface since that period of that year.
Success also means he has secured twenty-one titles at 21 different competitions.
"It's the first time I am participating in a event with my children together, so to win a title is particularly special," commented tennis professional the champion.
"This championship is in honour of my second daughter Victoria, because the maiden victory I achieved when my child my daughter was born was for her."
The athlete, the 2021 US Open champion, had lost his last six championship matches, comprising in that event earlier this year.
His defensive approach and regular emotional displays on court had prompted commentators to wonder if his ability to compete at the top level was concluded.
Yet the athlete has made changes in the last few weeks, striving to advance forward and perform aggressively, backed up by an enhanced service.
Medvedev came back from a deficit in the first set against the difficult opponent, winning 4 of the concluding five games to take the lead.
Both players traded breaks in the following set before the Frenchman, attempting for his initial ATP Tour victory, seized the initiative to create a third set.
The opponent saved 4 initial opportunities in a close third set before Medvedev secured a break to fifteen to secure the win.
Appropriately, he earned the title with a rally at the front of the court, with his opponent failing to control a volley after two hours and 38 minutes.
