Nineteen of Medvedev's twenty-one championships have been achieved on hard surfaces
A resurgent the Russian player won his first trophy for nearly 30 months with victory over opponent Moutet in the competition championship match.
The athlete, a former top-ranked player, has endured a challenging year, achieving just a single victory at the major tournaments and suffering a setback at the US Open.
The player's varied form on the tennis tour - and struggles with his serve in especial - led to him dropping out of the top ten and eventually parting ways with long-term mentor Gilles Cervara.
Now collaborating with Thomas Johansson and Rohan Goetzke, he has steadily progressed in the past month - climaxing in a tightly fought three-set win over Frenchman Corentin Moutet.
It is Medvedev's maiden championship after the 2023 Rome Masters and maiden on a hard court after spring of 2023.
The win also indicates Medvedev has achieved 21 championships at twenty-one various events.
"It's the first time I am participating in a competition with my children simultaneously, so to secure a title is really nice," stated world number 14 the champion.
"This championship is in tribute of my younger daughter Victoria, because the maiden victory I got when my first daughter Alisa was born was for her."
The athlete, the 2021 US Open champion, had lost his last six finals, featuring in the German tournament earlier this year.
The player's counter-punching play style and recurring emotional displays on court had led some to wonder if his skill to play at the highest level was finished.
But the athlete has made changes in the last few weeks, making an effort to advance forward and compete positively, supported by an better serve.
The champion fought back from a deficit in the first set against the difficult opponent, securing 4 of the final five exchanges to gain the advantage.
The competitors swapped breaks in the second set before the Frenchman, bidding for his maiden tour victory, seized the initiative to force a final set.
He rescued four initial opportunities in a competitive third set before Medvedev won the break to 15 to secure the win.
Suitably, the winner clinched the title with a rally at the front of the court, with his opponent failing to manage a shot after over two and a half hours.