Nineteen of Medvedev's 21 titles have been achieved on hardcourt
A comeback the Russian player won his maiden trophy for 882 days with victory over opponent Moutet in the competition final.
Medvedev, a former top-ranked player, has experienced a torrid period, winning just one match at the major tournaments and experiencing a meltdown at the New York tournament.
His varied form on the ATP Tour - and issues with his serving in particular - resulted in him dropping out of the world's top 10 and finally separating with former trainer Gilles Cervara.
Now collaborating with his coach and his other coach, the tennis star has consistently improved in the last few weeks - peaking in a tightly fought competitive triumph over Frenchman Corentin Moutet.
It is Medvedev's initial championship after the 2023 Rome Masters and initial on a hardcourt after March of that year.
The win also indicates Medvedev has secured 21 championships at 21 distinct tournaments.
"For the first time I'm at a competition with my two daughters simultaneously, so to win a trophy is really nice," said tennis professional Medvedev.
"This victory is in tribute of my second daughter her name, because the maiden victory I achieved when my older daughter Alisa was born was for her."
The athlete, the past champion, had failed in his last six finals, including in that event previously this season.
Medvedev's defensive strategy and regular outbursts on the tennis court had caused observers to doubt if his capacity to compete at the highest level was finished.
But the player has made changes in the past month, striving to come to the net and play aggressively, supported by an enhanced service.
The champion recovered from a deficit in the opening set against the difficult opponent, taking 4 of the final five games to take the lead.
The pair exchanged break points in the following set before the Frenchman, bidding for his maiden tour victory, took control to create a final set.
He defended 4 initial opportunities in a tight deciding set before the champion won the break to fifteen to serve for the match.
Appropriately, he secured the win with a shot at the net, with his opponent unable to manage a return after a lengthy match.
