Nineteen of the Russian's twenty-one titles have been earned on hard courts
A comeback the Russian player won his maiden trophy for nearly 30 months with victory over opponent Moutet in the Almaty Open title decider.
The athlete, a ex- number one, has had a difficult year, winning just one win at the big events and undergoing a meltdown at the New York tournament.
Medvedev's unpredictability on the professional circuit - and issues with his serving in especial - resulted in him exiting of the world's top 10 and finally separating with long-time mentor Gilles Cervara.
Now working with Thomas Johansson and Rohan Goetzke, the tennis star has gradually advanced in the recent weeks - climaxing in a tightly fought competitive win over Frenchman Moutet.
This marks Medvedev's first trophy since the Rome competition and initial on a hard surface from spring of 2023.
The win also signifies Medvedev has achieved twenty-one victories at 21 various tournaments.
"It's the first time I'm at a event with my two daughters together, so to win a title is particularly special," said ranked player the champion.
"This title is in honour of my child Victoria, because the first title I got when my child my daughter was born was for her."
Medvedev, the 2021 US Open champion, had been defeated in his previous six finals, comprising in that event in the past months.
His retrieving play style and recurring emotional displays on the tennis court had led some to question if his ability to perform at the top level was over.
Yet the athlete has made changes in the last few weeks, making an effort to approach the net and play assertively, backed up by an better serve.
Medvedev fought back from a break down in the opening set against the tricky Frenchman, taking 4 of the concluding five points to gain the advantage.
The pair traded breaks in the middle set before the Frenchman, striving for his initial tour title, seized the initiative to create a decider.
The opponent saved four initial opportunities in a competitive deciding set before Medvedev broke to 15 to secure the win.
Fittingly, he earned the title with a rally at the net, with Moutet incapable to control a shot after over two and a half hours.