Nineteen of the Russian's 21 championships have been won on hard courts
A comeback Medvedev won his maiden trophy for nearly 30 months with victory over opponent Moutet in the competition championship match.
The Russian, a former world number one, has endured a difficult year, achieving just a single victory at the major tournaments and experiencing a setback at the US Open.
The player's inconsistency on the professional circuit - and difficulties with his service game in specific - caused him dropping out of the world's top 10 and ultimately parting ways with long-term trainer Gilles Cervara.
Presently collaborating with his coach and his other coach, the tennis star has consistently advanced in the last few weeks - peaking in a closely contested 7-5 4-6 6-3 victory over opponent Moutet.
It is Medvedev's maiden championship following the Rome competition and first on a hard surface from March of the previous year.
Success also indicates he has secured twenty-one victories at 21 various competitions.
"It's the first time I have attended a event with my two daughters simultaneously, so to win a championship is particularly special," said tennis professional the champion.
"This championship is in dedication of my second daughter my daughter, because the initial championship I achieved when my child her name was born was for her."
The tennis star, the former major winner, had lost his past six championship matches, featuring in that event in the past months.
His counter-punching strategy and regular emotional displays on the tennis court had led commentators to doubt if his skill to play at the elite level was concluded.
But the athlete has made changes in recent weeks, making an effort to approach the net and compete positively, reinforced by an better serving game.
The champion came back from a break down in the opening set against the tricky Frenchman, taking 4 of the last five exchanges to take the lead.
The pair exchanged breaks in the following set before the Frenchman, striving for his maiden professional championship, gained dominance to push for a third set.
Moutet saved four early opportunities in a tight third set before Medvedev secured a break to that score to close out the victory.
Fittingly, Medvedev earned the win with a rally at the net area, with his opponent failing to control a return after over two and a half hours.
