19 of the Russian's 21 victories have been won on hard courts
A revitalized Medvedev claimed his first trophy for 882 days with success over opponent Moutet in the tournament championship match.
The athlete, a ex- top-ranked player, has had a challenging period, winning just one match at the major tournaments and undergoing a setback at the American major.
His unpredictability on the tennis tour - and difficulties with his serving in especial - led to him dropping out of the top ten and ultimately separating with long-term trainer Gilles Cervara.
Now training with Johansson and his other coach, the tennis star has consistently advanced in the past month - peaking in a hard-fought three-set victory over opponent Moutet.
It is Medvedev's first championship after the Italian tournament and first on a hardcourt after spring of the previous year.
The win also signifies he has secured twenty-one championships at 21 distinct competitions.
"For the first time I'm at a competition with my both daughters simultaneously, so to get a championship is particularly special," said ranked player Medvedev.
"This championship is in honour of my younger daughter Victoria, because the initial championship I got when my older daughter Alisa was delivered was for her."
The athlete, the former major winner, had been defeated in his previous six finals, including in Halle earlier this year.
Medvedev's defensive approach and recurring outbursts on the tennis court had caused commentators to question if his capacity to play at the top level was finished.
But the 29-year-old has made changes in the last few weeks, making an effort to advance forward and play aggressively, supported by an better serve.
He fought back from a disadvantage in the initial set against the tricky Frenchman, taking 4 of the concluding five points to gain the advantage.
The competitors exchanged break points in the second set before the Frenchman, bidding for his first professional championship, seized the initiative to force a final set.
He rescued 4 initial break points in a competitive final set before the Russian broke to 15 to secure the win.
Appropriately, he secured victory with a rally at the net, with Moutet incapable to manage a volley after two hours and 38 minutes.
